Method and system for fabricating object featuring properties of a blood vessel

ABSTRACT

A tubular structure fabricated by additive manufacturing from non-biological building material formulations, and featuring an elongated core, a shell encapsulating the core and an intermediate shell between the core and the shell. Each of the core, the shell and the intermediate shell is made of a different material or a different combination of materials. Both the core and the intermediate shell are sacrificial. Additive manufacturing of the tubular structure is usable for fabricating an object featuring properties of a blood vessel.

RELATED APPLICATIONS

This application is a division of U.S. patent application Ser. No.16/634,582 filed on Jan. 28, 2020, which is a National Phase of PCTPatent Application No. PCT/IL2018/050840 having International FilingDate of Jul. 27, 2018, which claims the benefit of priority under 35 USC§ 119(e) of U.S. Provisional Patent Application No. 62/538,015 filed onJul. 28, 2017 which was co-filed with U.S. Provisional PatentApplication Nos. 62/538,003, 62/538,018, 62/538,006 and 62/538,026.

The contents of the above applications are all incorporated by referenceas if fully set forth herein in their entirety.

FIELD AND BACKGROUND OF THE INVENTION

The present invention, in some embodiments thereof, relates to additivemanufacturing and, more particularly, but not exclusively, to a methodand system for fabricating object featuring properties of a blood vesselby additive manufacturing.

Additive manufacturing (AM) is generally a process in which athree-dimensional (3D) object is manufactured utilizing a computer modelof the objects. Such a process is used in various fields, such as designrelated fields for purposes of visualization, demonstration andmechanical prototyping, as well as for rapid manufacturing (RM). Thebasic operation of any AM system consists of slicing a three-dimensionalcomputer model into thin cross sections, translating the result intotwo-dimensional position data and feeding the data to control equipmentwhich manufacture a three-dimensional structure in a layerwise manner.

One type of AM is three-dimensional inkjet printing processes. In thisprocess, a building material is dispensed from a dispensing head havinga set of nozzles to deposit layers on a supporting structure. Dependingon the building material, the layers may then be cured or solidifiedusing a suitable device.

Various three-dimensional inkjet printing techniques exist and aredisclosed in, e.g., U.S. Pat. Nos. 6,259,962, 6,569,373, 6,658,314,6,850,334, 7,183,335, 7,209,797, 7,225,045, 7,300,619, 7,479,510,7,500,846, 7,962,237.

Several AM processes allow additive formation of objects using more thanone modeling material. For example, U.S. Pat. No. 9,031,680 of thepresent Assignee, discloses a system which comprises a solid freeformfabrication apparatus having a plurality of dispensing heads, a buildingmaterial supply apparatus configured to supply a plurality of buildingmaterials to the fabrication apparatus, and a control unit configuredfor controlling the fabrication and supply apparatus. The system hasseveral operation modes. In one mode, all dispensing heads operateduring a single building scan cycle of the fabrication apparatus. Inanother mode, one or more of the dispensing heads is not operativeduring a single building scan cycle or part thereof.

The building materials may include modeling materials and supportmaterials, which form the object and the temporary support constructionssupporting the object as it is being built, respectively.

The modeling material (which may include one or more material(s),included in one or more formulations) is deposited to produce thedesired object/s.

The support material, also known in the art as “supporting material”,(which may include one or more material(s)) is used, with or withoutmodeling material elements, is used to support specific areas of theobject during building and for assuring adequate vertical placement ofsubsequent object layers. For example, in cases where objects includeoverhanging features or shapes, e.g. curved geometries, negative angles,voids, and the like, objects are typically constructed using adjacentsupport constructions, which are used during the printing.

In all cases, the support material is deposited in proximity of themodeling material, enabling the formation of complex object geometriesand filling of object voids.

In all of the currently practiced technologies, the deposited supportmaterial and modeling material are hardened, typically upon exposure toa curing condition (e.g., curing energy), to form the required layershape. After printing completion, support structures are removed toreveal the final shape of the fabricated 3D object.

When using currently available commercial print heads, such as ink-jetprinting heads, the support material should have a relatively lowviscosity (about 10-20 cPs) at the working, i.e., jetting, temperature,such that it can be jetted. Further, the support material should hardenrapidly in order to allow building of subsequent layers. Additionally,the hardened support material should have sufficient mechanical strengthfor holding the model material in place, and low distortion for avoidinggeometrical defects.

Known methods for removal of support materials include mechanical impact(applied by a tool or water-jet), as well as chemical methods, such asdissolution in a solvent, with or without heating. The mechanicalmethods are labor intensive and are often unsuited for small intricateparts.

For dissolving the support materials, the fabricated object is oftenimmersed in water or in a solvent that is capable of dissolving thesupport materials. The solutions utilized for dissolving the supportmaterial are also referred to herein and in the art as “cleaningsolutions”. In many cases, however, the support removal process mayinvolve hazardous materials, manual labor and/or special equipmentrequiring trained personnel, protective clothing and expensive wastedisposal. In addition, the dissolution process is usually limited bydiffusion kinetics and may require very long periods of time, especiallywhen the support constructions are large and bulky. Furthermore,post-processing may be necessary to remove traces of a ‘mix layer’ onobject surfaces. The term “mix layer” refers to a residual layer ofmixed hardened model and support materials formed at the interfacebetween the two materials on the surfaces of the object beingfabricated, by model and support materials mixing into each other at theinterface between them.

Additionally, methods requiring high temperatures during support removalmay be problematic since there are model materials that aretemperature-sensitive, such as waxes and certain flexible materials.Both mechanical and dissolution methods for removal of support materialsare especially problematic for use in an office environment, whereease-of-use, cleanliness and environmental safety are majorconsiderations.

Water-soluble materials for 3D building are described, for example, inU.S. Pat. No. 6,228,923, where a water soluble thermoplasticpolymer—Poly(2-ethyl-2-oxazoline)—is taught as a support material in a3D building process involving high pressure and high temperatureextrusion of ribbons of selected materials onto a plate.

A water-containing support material comprising a fusible crystal hydrateis described in U.S. Pat. No. 7,255,825.

Formulations suitable for forming a hardened support material inbuilding a 3D object are described, for example, in U.S. Pat. Nos.7,479,510, 7,183,335 and 6,569,373, all to the present Assignee.Generally, the compositions disclosed in these patents comprise at leastone UV curable (reactive) component, e.g., an acrylic component, atleast one non-UV curable component, e.g. a polyol or glycol component,and a photoinitiator. After irradiation, these compositions provide asemi-solid or gel-like material capable of dissolving or swelling uponexposure to water, to an alkaline or acidic solution or to a waterdetergent solution.

Besides swelling, another characteristic of such a support material maybe the ability to break down during exposure to water, to an alkaline oracidic solution or to a water detergent solution because the supportmaterial is made of hydrophilic components. During the swelling process,internal forces cause fractures and breakdown of the hardened support.In addition, the support material can contain a substance that liberatesbubbles upon exposure to water, e.g. sodium bicarbonate, whichtransforms into CO₂ when in contact with an acidic solution. The bubblesaid in the process of removal of support from the model.

Several additive manufacturing processes allow additive formation ofobjects using more than one modeling material. For example, U.S. patentapplication having Publication No. 2010/0191360, of the presentAssignee, discloses a system which comprises a solid freeformfabrication apparatus having a plurality of dispensing heads, a buildingmaterial supply apparatus configured to supply a plurality of buildingmaterials to the fabrication apparatus, and a control unit configuredfor controlling the fabrication and supply apparatus. The system hasseveral operation modes. In one mode, all dispensing heads operateduring a single building scan cycle of the fabrication apparatus. Inanother mode, one or more of the dispensing heads is not operativeduring a single building scan cycle or part thereof.

In a 3D inkjet printing process such as Polyjet™ (Stratasys Ltd.,Israel), the building material is selectively jetted from one or moreprinting heads and deposited onto a fabrication tray in consecutivelayers according to a pre-determined configuration as defined by asoftware file.

U.S. Pat. No. 9,227,365, by the present assignee, discloses methods andsystems for solid freeform fabrication of shelled objects, constructedfrom a plurality of layers and a layered core constituting core regionsand a layered shell constituting envelope regions.

Additive Manufacturing processes have been used to form rubber-likematerials. For example, rubber-like materials are used in PolyJet™systems as described herein. These materials are formulated to haverelatively low viscosity permitting dispensing, for example by inkjet,and to develop Tg which is lower than room temperature, e.g., −10° C. orlower. The latter is obtained by formulating a product with relativelylow degree of cross-linking and by using monomers and oligomers withintrinsic flexible molecular structure (e.g., acrylic elastomers).

An exemplary family of Rubber-like materials usable in PolyJet™ systems(marketed under the trade name “Tango™” family) offers a variety ofelastomer characteristics of the obtained hardened material, includingShore A hardness, Elongation at break, Tear Resistance and Tensilestrength. The softest material in this family features a Shore Ahardness of 27.

Another family of Rubber-like materials usable in PolyJet™ systems(marketed under the trade name “Agilus™” family) is described in PCTInternational Application No. IL2017/050604 (Published asWO2017/208238), by the present assignee, and utilizes a curableelastomeric formulation that comprises an elastomeric curable materialand silica particles.

SUMMARY OF THE INVENTION

According to an aspect of some embodiments of the present inventionthere is provided a tubular structure fabricated by additivemanufacturing from non-biological building material formulations, andcomprises: an elongated core, a shell encapsulating the core and anintermediate shell between the core and the shell, wherein each of thecore, the shell and the intermediate shell is made of a differentmaterial or a different combination of materials, and wherein both thecore and the intermediate shell are sacrificial.

According to some of any of the embodiments of the invention theintermediate shell is made of a hardened support material (e.g.,Material S), and the core is made of a liquid or liquid-like material(e.g., Material L).

According to some embodiments of the invention the core is made of ahardened support material (e.g., Material S), and the intermediate shellis made of a liquid or liquid-like material (e.g., Material L).

According to some of any of the embodiments of the invention the liquidor liquid-like material L is characterized by at least one of: aviscosity of no more than 10000 centipoises; Shear loss modulus to Shearstorage modulus ratio greater than 1; a Shear modulus lower than 20 kPa;flowability when subjected to a positive pressure of no more than 1 bar;a shear-thinning and/or thixotropic behavior; and a thermal-thinningbehavior.

According to some of any of the embodiments of the invention the tubularstructure has a shape of a blood vessel.

According to some of any of the embodiments of the invention the shellis embedded in a supporting structure.

According to some of any of the embodiments of the invention thesupporting structure is sacrificial.

According to an aspect of some embodiments of the present inventionthere is provided an object fabricated by additive manufacturing fromnon-biological building material formulations, the object has a shape ofan organ and comprises: at least one structure having a shape of a bloodvessel and at least one structure having a shape of a bodily structureother than a blood vessel, wherein the structure having the shape of theblood vessel is the tubular structure as delineated above and optionallyand preferably as further detailed hereinabove.

According to an aspect of some embodiments of the present inventionthere is provided an object fabricated by additive manufacturing fromnon-biological building material formulations, the object comprises aninterconnected network of elongated structures, each having a shape of ablood vessel and being is the tubular structure as delineated above andoptionally and preferably as further detailed hereinabove.

According to some of any of the embodiments of the invention the tubularstructure comprises reinforcing elements embedded in the shell.

According to some of any of the embodiments of the invention thereinforcing elements are oriented to effect anisotropic mechanicalproperties of the shell.

According to some of any of the embodiments of the invention thereinforcing elements comprise at least one elongated reinforcing elementembedded in the shell parallel to a longitudinal axis of the shell.

According to some of any of the embodiments of the invention thereinforcing elements comprise at least one annular reinforcing elementembedded in the shell along an azimuthal direction defining the shell.

According to some of any of the embodiments of the invention the tubularstructure comprises a liner layer at least partially coating an innersurface of the shell, between the intermediate shell and the innersurface, wherein an attachment between the liner layer and the shell isstronger than an attachment between the intermediate shell and the linerlayer.

According to some of any of the embodiments of the invention the linerlayer is harder than the shell.

According to some of any of the embodiments of the invention the linerlayer has mechanical properties of plaque tissue.

According to an aspect of some embodiments of the present inventionthere is provided a method of additive manufacturing of at least onetubular structure featuring properties of a blood vessel, the methodcomprises: receiving as input image data describing a shape of a bloodvessel; converting the image data to computer object data; receiving asinput hardness levels along the blood vessel; accessing a computerreadable medium storing a lookup table having a plurality of entrieseach corresponding to a different range of hardness levels, and beingassociated with at least one additive manufacturing parameter selectedfrom the group consisting of a building material formulation, acombination of building material formulations, and a wall thickness;extracting additive manufacturing parameters from the lookup table basedon the input hardness levels; and operating an additive manufacturingsystem according to the extracted additive manufacturing parameter toform a plurality of layers in a configured pattern corresponding to theshape of the blood vessel.

According to some of any of the embodiments of the invention operatingthe additive manufacturing system comprises forming an elongated core, ashell encapsulating the core and having the shape of the blood vessel,and an intermediate shell between the core and the shell, wherein eachof the core, the shell and the intermediate shell is formed bydispensing a different building material formulation or a differentcombination of building material formulations, and wherein both the coreand the intermediate shell are sacrificial.

According to an aspect of some embodiments of the present inventionthere is provided a method of additive manufacturing of at least onetubular structure featuring properties of a blood vessel, the bloodvessel being described by computer object data, the method comprises:dispensing a plurality of different building material formulations toform a plurality of layers in a configured pattern to form an elongatedcore, a shell encapsulating the core and having the shape of the bloodvessel, and an intermediate shell between the core and the shell,wherein each of the core, the shell and the intermediate shell is formedby dispensing a different building material formulation or a differentcombination of building material formulations, and wherein both the coreand the intermediate shell are sacrificial.

According to some of any of the embodiments of the invention the methodcomprises, subsequent to the dispensing, exposing the layers to a curingcondition, to thereby obtain at least a hardened material forming theshell.

According to some of any of the embodiments of the invention the methodcomprises removing the core and the intermediate shell.

According to some of any of the embodiments of the invention one of thecore and the intermediate shell is formed by dispensing a buildingmaterial formulation which provides, upon exposure to a curingcondition, a liquid or liquid-like material characterized by at leastone of: a viscosity of no more than 10000 centipoises; Shear lossmodulus to Shear storage modulus ratio greater than 1; a Shear moduluslower than 20 kPa; flowability when subjected to a positive pressure ofno more than 1 bar; a shear-thinning and/or thixotropic behavior; and athermal-thinning behavior. A liquid or liquid-like material as describedherein is also referred to herein interchangeably as Material L.

According to some of any of the embodiments of the invention one of thecore and the intermediate shell is formed by dispensing a buildingmaterial formulation which comprises a non-curable material, thebuilding material formulation provides a liquid or liquid-like material(e.g., Material L). Such a building formulation is also referred toherein interchangeably as “Formulation L” or as “liquid formulation”.

According to some of any of the embodiments of the invention thenon-curable material comprises a poly(alkylene glycol) having amolecular weight of less than 2000 grams/mol.

According to some of any of the embodiments of the invention thebuilding material formulation (e.g., Formulation L) which comprises thenon-curable material, also comprises a curable material.

According to some of any of the embodiments of the invention the curablematerial comprises a mono-functional curable material.

According to some of any of the embodiments of the invention the curablematerial is hydrophilic.

According to some of any of the embodiments of the invention the curablematerial, when hardened, provides a shear-thinning and/or thixotropicmaterial.

According to some of any of the embodiments of the invention the curablematerial, when hardened, provides a thermal-thinning material.

According to some of any of the embodiments of the invention the curablematerial, when hardened, provides a water-soluble or water-immisciblematerial.

According to some of any of the embodiments of the invention an amountof the curable material in the building material formulation (e.g.,Formulation L) ranges from 10% to 25%.

According to some of any of the embodiments of the invention one of thecore and the intermediate shell is formed by dispensing a buildingmaterial formulation which provides, when hardened or when exposed to acuring condition, a water-soluble or water-miscible material.

According to some of any of the embodiments of the invention one of thecore and the intermediate shell is formed by dispensing a buildingmaterial formulation which provides, when hardened or when exposed to acuring condition, a material selected from a shear-thinning material, athixotropic material or a thermal-thinning material.

According to some of any of the embodiments of the invention the methodcomprises removing the core and the intermediate shell.

According to some embodiments of the invention the method comprises:generating computer object data describing cavities in the blood vessel,generating computer object data describing the cavities in shrunk form,and combining the computer object data describing the blood vessel withthe computer object data describing the cavities in the shrunk form, toprovide combined computer object data describing the blood vessel and acore encapsulated by the hollow structure in a manner that there is agap between an inner surface of the blood vessel and an outermostsurface of the core.

Unless otherwise defined, all technical and/or scientific terms usedherein have the same meaning as commonly understood by one of ordinaryskill in the art to which the invention pertains. Although methods andmaterials similar or equivalent to those described herein can be used inthe practice or testing of embodiments of the invention, exemplarymethods and/or materials are described below. In case of conflict, thepatent specification, including definitions, will control. In addition,the materials, methods, and examples are illustrative only and are notintended to be necessarily limiting.

Implementation of the method and/or system of embodiments of theinvention can involve performing or completing selected tasks manually,automatically, or a combination thereof. Moreover, according to actualinstrumentation and equipment of embodiments of the method and/or systemof the invention, several selected tasks could be implemented byhardware, by software or by firmware or by a combination thereof usingan operating system.

For example, hardware for performing selected tasks according toembodiments of the invention could be implemented as a chip or acircuit. As software, selected tasks according to embodiments of theinvention could be implemented as a plurality of software instructionsbeing executed by a computer using any suitable operating system. In anexemplary embodiment of the invention, one or more tasks according toexemplary embodiments of method and/or system as described herein areperformed by a data processor, such as a computing platform forexecuting a plurality of instructions. Optionally, the data processorincludes a volatile memory for storing instructions and/or data and/or anon-volatile storage, for example, a magnetic hard-disk and/or removablemedia, for storing instructions and/or data. Optionally, a networkconnection is provided as well. A display and/or a user input devicesuch as a keyboard or mouse are optionally provided as well.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Some embodiments of the invention are herein described, by way ofexample only, with reference to the accompanying drawings and images.With specific reference now to the drawings in detail, it is stressedthat the particulars shown are by way of example and for purposes ofillustrative discussion of embodiments of the invention. In this regard,the description taken with the drawings makes apparent to those skilledin the art how embodiments of the invention may be practiced.

In the drawings:

FIGS. 1A-1D are schematic illustrations of an additive manufacturingsystem according to some embodiments of the invention.

FIGS. 2A-2C are schematic illustrations of printing heads according tosome embodiments of the present invention.

FIGS. 3A and 3B are schematic illustrations demonstrating coordinatetransformations according to some embodiments of the present invention.

FIG. 4 is a schematic illustration of a tubular structure according tosome embodiments of the present invention.

FIG. 5 is a schematic illustration defining parameters that can be usedaccording to some embodiments of the present invention forcharacterizing dimensions of a core and an intermediate shell, accordingto some embodiments of the present invention.

FIG. 6 is a schematic illustration of the tubular structure inembodiments in which the shell of the tubular structure is embedded in asupporting structure.

FIGS. 7A-7C are schematic illustrations of the tubular structure inembodiments of the invention in which the tubular structure comprisesreinforcing elements embedded in its shell.

FIG. 8 is a schematic illustration of the tubular structure in acut-open view, in embodiments of the invention in which the tubularstructure comprises a liner layer at least partially coating an innersurface of the shell.

FIG. 9 is an example of a system for printing a 3D part using GPUmaterial assignment based on distance fields.

FIG. 10 is a block diagram of an exemplary computer architecture for thecomputer of FIG. 9 .

FIG. 11 is a flow diagram of a method of converting a 3D model intoprint instructions and printing a 3D part.

FIG. 12 is a block diagram of elements used in the method of FIG. 11 .

FIG. 13 is a perspective view of a portion of a part showing texture anda bump.

FIG. 14 is a perspective view of a build space with an oriented part.

FIG. 15 is a method of determining a distance field value.

FIG. 16 is a top view of a slice in the build space showing thedetermination of a distance field value.

FIG. 17 is a flow diagram of a method of performing initial steps ofmaterial selection.

FIG. 18 provides a side view of a part showing different supportregions.

FIG. 19 provides a method of selecting a material for a voxel when thereis only one part.

FIG. 20 provides a method of selecting a material for a voxel when thereare multiple parts in the build space.

FIG. 21 provides a sectional view of a part constructed through thevarious embodiments showing a single part in the build space.

FIG. 22 provides a side view of two parts showing the removal ofinterference through the selection of a single part's material selectionrules.

FIG. 23 shows a merged area where two different modulating functions aremerged together.

FIG. 24 shows a merged area where two different materials are mergedtogether.

FIG. 25 is a schematic illustration of an object fabricated by additivemanufacturing from non-biological building material formulations,according to some embodiments of the present invention.

FIG. 26 is an image of an interconnected network of elongatedstructures, fabricated according to some embodiments of the presentinvention by additive manufacturing from non-biological buildingmaterial formulations.

FIG. 27 is a flowchart diagram of a method of additive manufacturing ofat least one tubular structure featuring properties of a blood vessel,according to some embodiments of the present invention.

FIGS. 28A and 28B are flowchart diagrams describing an exemplifiedprocedure which can be used according to some embodiments of the presentinvention for obtaining computer object data.

FIGS. 29A-29D are visualized computer object data (FIG. 29A and images(FIGS. 29B-29D) of tubes array (FIG. 29A), printed tubes of varyingcomposition (FIG. 29B), linear and curved tube geometries (FIG. 29C),and Theresa Aneurysm (FIG. 29D), obtained in experiments performedaccording to some embodiments of the present invention.

FIG. 30 shows results of experiments conducted according to someembodiments of the present invention to investigate the effect of wallthickness on properties of printed tubes.

FIG. 31 is a graph presenting Stress vs Strain Curves obtained inexperiments performed according to some embodiments of the presentinvention.

FIGS. 32A-32C show results of experiments conducted according to someembodiments of the present invention to investigate the effect ofreinforcement on properties of printed tubes.

FIG. 33 is a schematic illustration of oriented reinforcing elementsused in experiments performed according to some embodiments of thepresent invention.

FIGS. 34A and 34B are schematic illustrations of encapsulated vesselspecimens used in experiments performed according to some embodiments ofthe present invention.

FIG. 35 shows results of a compliance test as a function of the innerdiameter of tubes, obtained in experiments performed according to someembodiments of the present invention.

FIG. 36 results of a compliance test as a function of the wall thicknessobtained in experiments performed according to some embodiments of thepresent invention.

FIG. 37 shows results of compliance and time-to-rupture (TTR)measurements for various printed tubes, as obtained in experimentsperformed according to some embodiments of the present invention.

FIG. 38 shows results of experiments performed according to someembodiments of the present invention to investigate the effect of adigital material used in a printing process on the compliance.

FIGS. 39A-39K are schematic illustrations describing an exemplifiedprocedure suitable for generating computer object data describing ahollow object.

DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION

The present invention, in some embodiments thereof, relates to additivemanufacturing and, more particularly, but not exclusively, to a methodand system for fabricating object featuring properties of a blood vesselby additive manufacturing.

Before explaining at least one embodiment of the invention in detail, itis to be understood that the invention is not necessarily limited in itsapplication to the details of construction and the arrangement of thecomponents and/or methods set forth in the following description and/orillustrated in the drawings and/or the Examples. The invention iscapable of other embodiments or of being practiced or carried out invarious ways.

Before explaining at least one embodiment of the invention in detail, itis to be understood that the invention is not necessarily limited in itsapplication to the details of construction and the arrangement of thecomponents and/or methods set forth in the following description and/orillustrated in the drawings and/or the Examples. The invention iscapable of other embodiments or of being practiced or carried out invarious ways.

The method and system of the present embodiments manufacturethree-dimensional objects based on computer object data in a layerwisemanner by forming a plurality of layers in a configured patterncorresponding to the shape of the objects. The computer object data canbe in any known format, including, without limitation, a StandardTessellation Language (STL) or a StereoLithography Contour (SLC) format,Virtual Reality Modeling Language (VRML), Additive Manufacturing File(AMF) format, Drawing Exchange Format (DXF), Polygon File Format (PLY)or any other format suitable for Computer-Aided Design (CAD).

The term “object” as used herein refers to a whole object or a partthereof.

Each layer is formed by additive manufacturing apparatus which scans atwo-dimensional surface and patterns it. While scanning, the apparatusvisits a plurality of target locations on the two-dimensional layer orsurface, and decides, for each target location or a group of targetlocations, whether or not the target location or group of targetlocations is to be occupied by building material formulation, and whichtype of building material formulation is to be delivered thereto. Thedecision is made according to a computer image of the surface.

In preferred embodiments of the present invention the AM comprisesthree-dimensional printing, more preferably three-dimensional inkjetprinting. In these embodiments a building material formulation isdispensed from a dispensing head having a set of nozzles to depositbuilding material formulation in layers on a supporting structure. TheAM apparatus thus dispenses building material formulation in targetlocations which are to be occupied and leaves other target locationsvoid. The apparatus typically includes a plurality of dispensing heads,each of which can be configured to dispense a different buildingmaterial formulation. Thus, different target locations can be occupiedby different building material formulations.

Herein throughout, the phrase “uncured building material” collectivelydescribes the materials that are dispensed during the fabricationprocess so as to sequentially form the layers, as described herein. Thisphrase encompasses uncured materials (also referred to herein asbuilding material formulation(s)) dispensed so as to form the printedobject, namely, one or more uncured modeling material formulation(s),and uncured materials dispensed so as to form the support, namelyuncured support material formulations.

The types of building material formulations can be categorized into twomajor categories: modeling material formulation and support materialformulation. The support material formulation can serve as a supportingmatrix or construction for supporting the object or object parts duringthe fabrication process and/or other purposes, e.g., providing hollow orporous objects. Support constructions may additionally include modelingmaterial formulation elements, e.g. for further support strength. Abuilding material formulation that provides a liquid or liquid-likematerial upon exposure to a curing condition can also be categorized,according to some embodiments of the present invention as a supportmaterial formulation.

Herein throughout, the phrases “cured modeling material” and “hardenedmodeling material” or simply “modeling material”, which are usedinterchangeably, describe the part of the building material that forms amodel object, as defined herein, upon exposing the dispensed buildingmaterial to curing, and following removal of the support material. Thecured or hardened modeling material can be a single hardened material ora mixture of two or more hardened materials, depending on the modelingmaterial formulations used in the method, as described herein. Abuilding material formulation that provides a liquid or liquid-likematerial upon exposure to a curing condition can also be categorized,according to some embodiments of the present invention as a modelingmaterial formulation.

Herein throughout, the phrase “modeling material formulation”, which isalso referred to herein interchangeably as “modeling formulation”,describes a part of the uncured building material which is dispensed soas to form the model object, as described herein. The modelingformulation is an uncured modeling formulation, which, upon exposure toa curing condition, forms the final object or a part thereof.

An uncured building material can comprise one or more modelingformulations, and can be dispensed such that different parts of themodel object are made upon curing different modeling formulations, andhence are made of different cured modeling materials or differentmixtures of cured modeling materials.

Herein throughout, the phrase “hardened support material” is alsoreferred to herein interchangeably as “cured support material” or simplyas “support material” and describes the part of the building materialthat is intended to support the fabricated final object during thefabrication process, and which is removed once the process is completedand a hardened modeling material is obtained.

Herein throughout, the phrase “support material formulation”, which isalso referred to herein interchangeably as “support formulation” orsimply as “formulation”, describes a part of the uncured buildingmaterial which is dispensed so as to form the support material, asdescribed herein. The support material formulation is an uncuredformulation. When a support material formulation is a curableformulation, it forms, upon exposure to a curing condition, a hardenedsupport material.

Support materials, which can be either liquid or liquid-like materialsor hardened, typically gel or gel-like materials, are also referred toherein as sacrificial materials, which are removable after layers aredispensed and exposed to a curing energy, to thereby expose the shape ofthe final object.

Herein and in the art, the term “gel” describes a material, oftenreferred to as a semi-solid material, which comprises athree-dimensional solid network, typically made of fibrous structureschemically or physically linked therebetween, and a liquid phase encagedwithin this network. Gels are typically characterized by a consistencyof a solid (e.g., are non-fluidic), and feature relatively low Tensilestrength, relatively low Shear Modulus, e.g., lower than 100 kPa, and aShear Loss Modulus to Shear Storage modulus (tan delta, G″/G′) valuelower than 1. Gels can be characterized as flowable when subjected to apositive pressure of at least 0.5 bar, preferably at least 1 bar, orhigher, or, alternatively, as non-flowable when subject to a pressurelower than 1 bar or lower than 0.5 bar or of 0.3 bar or lower.

Gel-like materials according to the present embodiments are typicallysoft materials, which can be gels or solids, which feature mechanicaland rheological properties of a gel.

Currently practiced support materials typically comprise a mixture ofcurable and non-curable materials, and are also referred to herein asgel-like support material or as gel support material.

Currently practiced support materials are typically water miscible, orwater-dispersible or water-soluble.

Herein throughout, the term “water-miscible” describes a material whichis at least partially dissolvable or dispersible in water, that is, atleast 50% of the molecules move into the water upon mixture. This termencompasses the terms “water-soluble” and “water dispersible”.

Herein throughout, the term “water-soluble” describes a material thatwhen mixed with water in equal volumes or weights, a homogeneoussolution is formed.

Herein throughout, the term “water-dispersible” describes a materialthat forms a homogeneous dispersion when mixed with water in equalvolumes or weights.

Herein throughout, the phrase “dissolution rate” describes a rate atwhich a substance is dissolved in a liquid medium. Dissolution rate canbe determined, in the context of the present embodiments, by the timeneeded to dissolve a certain amount of a support material. The measuredtime is referred to herein as “dissolution time”.

Herein throughout, whenever the phrase “weight percents” is indicated inthe context of embodiments of a formulation (e.g., a building materialformulation), it is meant weight percents of the total weight of therespective formulation or formulation system as described herein.

The phrase “weight percents” is also referred to herein as “% by weight”or “% wt.”

Herein throughout, some embodiments of the present invention aredescribed in the context of the additive manufacturing being a 3D inkjetprinting. However, other additive manufacturing processes, such as, butnot limited to, SLA and DLP, are contemplated.

An uncured building material can comprise one or more modelingformulations, and can be dispensed such that different parts of theobject are made, upon curing, of different cured modeling formulationsor different combinations thereof, and hence are made of different curedmodeling materials or different mixtures of cured modeling materials.

The formulations forming the building material (modeling materialformulations and optionally support material formulations) comprise oneor more curable materials, which, when exposed to a curing condition(e.g., curing energy), form hardened (e.g., cured, solidified) material.

Herein throughout, a “curable material” is a compound (typically amonomeric or oligomeric compound, yet optionally a polymeric material)which, when exposed to a curing condition (e.g., curing energy), asdescribed herein, solidifies or hardens to form a cured material.Curable materials are typically polymerizable materials, which undergopolymerization and/or cross-linking when exposed to suitable curingcondition, typically a source of energy.

A curable material, according to the present embodiments, can harden orsolidify (cure) while being exposed to a curing condition which can be acuring energy, and/or to another curing condition such as contact with achemical reagent or exposure to the environment.

The terms “curable” and “solidifiable” as used herein areinterchangeable.

According to some embodiments of the present invention, a curablematerial as described herein hardens upon undergoing polymerization, andis also referred to herein as a polymerizable material.

The polymerization can be, for example, free-radical polymerization,cationic polymerization or anionic polymerization, and each can beinduced when exposed to curing energy such as, for example, radiation,heat, etc., as described herein, or to a curing condition other thancuring energy.

In some of any of the embodiments described herein, a curable materialis a photopolymerizable material, which polymerizes and/or undergoescross-linking upon exposure to radiation, as described herein, and insome embodiments the curable material is a UV-curable material, whichpolymerizes and/or undergoes cross-linking upon exposure to UV or UV-visradiation, as described herein.

In some embodiments, a curable material as described herein is aphotopolymerizable material that polymerizes via photo-inducedfree-radical polymerization. Alternatively, the curable material is aphotopolymerizable material that polymerizes via photo-induced cationicpolymerization.

In some of any of the embodiments described herein, a curable materialcan be a monomer, an oligomer or a short-chain polymer, each beingpolymerizable and/or cross-linkable as described herein.

In some of any of the embodiments described herein, when a curablematerial is exposed to a curing condition (e.g., radiation), it hardens(solidifies, cures) by any one, or combination, of chain elongation andcross-linking.

In some of any of the embodiments described herein, a curable materialis a monomer or a mixture of monomers which can form a polymericmaterial upon a polymerization reaction, when exposed to a curingcondition (e.g., curing energy) at which the polymerization reactionoccurs. Such curable materials are also referred to herein as monomericcurable materials.

In some of any of the embodiments described herein, a curable materialis an oligomer or a mixture of oligomers which can form a polymericmaterial upon a polymerization reaction, when exposed to a curingcondition (e.g., curing energy) at which the polymerization reactionoccurs. Such curable materials are also referred to herein as oligomericcurable materials.

In some of any of the embodiments described herein, a curable material,whether monomeric or oligomeric, can be a mono-functional curablematerial or a multi-functional curable material.

Herein, a mono-functional curable material comprises one functionalgroup that can undergo polymerization when exposed to a curing conditionsuch as curing energy (e.g., radiation).

A multi-functional curable material comprises two or more, e.g., 2, 3, 4or more, functional groups that can undergo polymerization when exposedto curing energy. Multi-functional curable materials can be, forexample, di-functional, tri-functional or tetra-functional curablematerials, which comprise 2, 3 or 4 groups that can undergopolymerization, respectively. The two or more functional groups in amulti-functional curable material are typically linked to one another bya linking moiety, as defined herein. When the linking moiety is anoligomeric or polymeric moiety, the multi-functional group is anoligomeric or polymeric multi-functional curable material.Multi-functional curable materials can undergo polymerization whensubjected to curing energy and/or act as cross-linkers.

The final three-dimensional object is made of the modeling materialformulation or a combination of modeling material formulations ormodeling and support material formulations or modification thereof(e.g., following curing). All these operations are well-known to thoseskilled in the art of solid freeform fabrication.

In some exemplary embodiments of the invention an object is manufacturedby dispensing two or more different building material formulations, eachformulation from a different dispensing head of the AM. The buildingmaterial formulations are optionally and preferably deposited in layersduring the same pass of the printing heads. The formulations andcombination of formulations within the layer are selected according tothe desired properties of the object.

A representative and non-limiting example of a system 110 suitable forAM of an object 112 according to some embodiments of the presentinvention is illustrated in FIG. 1A. System 110 comprises an additivemanufacturing apparatus 114 having a dispensing unit 16 which comprisesa plurality of dispensing heads. Each head preferably comprises an arrayof one or more nozzles 122, as illustrated in FIGS. 2A-2C describedbelow, through which an uncured, liquid, building material formulation124 is dispensed.

Preferably, but not obligatorily, apparatus 114 is a three-dimensionalprinting apparatus, in which case the dispensing heads are printingheads, and the building material formulation is dispensed via inkjettechnology. This need not necessarily be the case, since, for someapplications, it may not be necessary for the additive manufacturingapparatus to employ three-dimensional printing techniques.Representative examples of additive manufacturing apparatus contemplatedaccording to various exemplary embodiments of the present inventioninclude, without limitation, fused deposition modeling apparatus andfused material formulation deposition apparatus.

Each dispensing head is optionally and preferably fed via a buildingmaterial formulation reservoir which may optionally include atemperature control unit (e.g., a temperature sensor and/or a heatingdevice), and a material formulation level sensor. To dispense thebuilding material formulation, a voltage signal is applied to thedispensing heads to selectively deposit droplets of material formulationvia the dispensing head nozzles, for example, as in piezoelectric inkjetprinting technology. The dispensing rate of each head depends on thenumber of nozzles, the type of nozzles and the applied voltage signalrate (frequency). Such dispensing heads are known to those skilled inthe art of solid freeform fabrication.

Preferably, but not obligatorily, the overall number of dispensingnozzles or nozzle arrays is selected such that half of the dispensingnozzles are designated to dispense support material formulation and halfof the dispensing nozzles are designated to dispense modeling materialformulation, i.e. the number of nozzles jetting modeling materialformulations is the same as the number of nozzles jetting supportmaterial formulation. In the representative example of FIG. 1A, fourdispensing heads 16 a, 16 b, 16 c and 16 d are illustrated. Each ofheads 16 a, 16 b, 16 c and 16 d has a nozzle array. In this Example,heads 16 a and 16 b can be designated for modeling materialformulation/s and heads 16 c and 16 d can be designated for supportmaterial formulation. Thus, head 16 a can dispense a first modelingmaterial formulation, head 16 b can dispense a second modeling materialformulation and heads 16 c and 16 d can both dispense support materialformulation. Alternatively, head 16 b can dispense a support materialformulation. In an alternative embodiment, heads 16 c and 16 d, forexample, may be combined in a single head having two nozzle arrays fordepositing support material formulation.

Yet it is to be understood that it is not intended to limit the scope ofthe present invention and that the number of modeling materialformulation depositing heads (modeling heads) and the number of supportmaterial formulation depositing heads (support heads) may differ.Generally, the number of modeling heads, the number of support heads andthe number of nozzles in each respective head or head array are selectedsuch as to provide a predetermined ratio, a, between the maximaldispensing rate of the support material formulation and the maximaldispensing rate of modeling material formulation. The value of thepredetermined ratio, a, is preferably selected to ensure that in eachformed layer, the height of modeling material formulation equals theheight of support material formulation. Typical values for a are fromabout 0.6 to about 1.5.

For example, for a=1, the overall dispensing rate of support materialformulation is generally the same as the overall dispensing rate of themodeling material formulation when all modeling heads and support headsoperate.

In a preferred embodiment, there are M modeling heads each having marrays of p nozzles, and S support heads each having s arrays of qnozzles such that M×m×p=S×s×q. Each of the M×m modeling arrays and S×ssupport arrays can be manufactured as a separate physical unit, whichcan be assembled and disassembled from the group of arrays. In thisembodiment, each such array optionally and preferably comprises atemperature control unit and a material formulation level sensor of itsown, and receives an individually controlled voltage for its operation.

Apparatus 114 can further comprise a solidifying device 324 which caninclude any device configured to emit light, heat or the like that maycause the deposited material formulation to hardened. For example,solidifying device 324 can comprise one or more radiation sources, whichcan be, for example, an ultraviolet or visible or infrared lamp, orother sources of electromagnetic radiation, or electron beam source,depending on the modeling material formulation being used. In someembodiments of the present invention, solidifying device 324 serves forcuring or solidifying the modeling material formulation.

In some embodiments of the present invention apparatus 114 comprisescooling system 134 such as one or more fans or the like.

The dispensing head and radiation source are preferably mounted in aframe or block 128 which is preferably operative to reciprocally moveover a tray 360, which serves as the working surface. In someembodiments of the present invention the radiation sources are mountedin the block such that they follow in the wake of the dispensing headsto at least partially cure or solidify the material formulations justdispensed by the dispensing heads. Tray 360 is positioned horizontally.According to the common conventions an X-Y-Z Cartesian coordinate systemis selected such that the X-Y plane is parallel to tray 360. Tray 360 ispreferably configured to move vertically (along the Z direction),typically downward. In various exemplary embodiments of the invention,apparatus 114 further comprises one or more leveling devices 132, e.g. aroller 326. Leveling device 326 serves to straighten, level and/orestablish a thickness of the newly formed layer prior to the formationof the successive layer thereon. Leveling device 326 preferablycomprises a waste collection device 136 for collecting the excessmaterial formulation generated during leveling. Waste collection device136 may comprise any mechanism that delivers the material formulation toa waste tank or waste cartridge.

In use, the dispensing heads of unit 16 move in a scanning direction,which is referred to herein as the X direction, and selectively dispensebuilding material formulation in a predetermined configuration in thecourse of their passage over tray 360. The building material formulationtypically comprises one or more types of support material formulation(s)and one or more types of modeling material formulation(s). The passageof the dispensing heads of unit 16 is followed by the curing of themodeling material formulation(s) by radiation source 126. In the reversepassage of the heads, back to their starting point for the layer justdeposited, an additional dispensing of building material formulation(s)may be carried out, according to predetermined configuration. In theforward and/or reverse passages of the dispensing heads, the layer thusformed may be straightened by leveling device 326, which preferablyfollows the path of the dispensing heads in their forward and/or reversemovement. Once the dispensing heads return to their starting point alongthe X direction, they may move to another position along an indexingdirection, referred to herein as the Y direction, and continue to buildthe same layer by reciprocal movement along the X direction.Alternately, the dispensing heads may move in the Y direction betweenforward and reverse movements or after more than one forward-reversemovement. The series of scans performed by the dispensing heads tocomplete a single layer is referred to herein as a single scan cycle.

Once the layer is completed, tray 360 is lowered in the Z direction to apredetermined Z level, according to the desired thickness of the layersubsequently to be printed. The procedure is repeated to formthree-dimensional object 112 in a layerwise manner.

In another embodiment, tray 360 may be displaced in the Z directionbetween forward and reverse passages of the dispensing head of unit 16,within the layer. Such Z displacement is carried out in order to causecontact of the leveling device with the surface in one direction andprevent contact in the other direction.

System 110 optionally and preferably comprises a building materialformulation supply system 330 which comprises the building materialformulation containers or cartridges and supplies a plurality ofbuilding material formulations to fabrication apparatus 114.

A control unit 340 controls fabrication apparatus 114 and optionally andpreferably also supply system 330. Control unit 340 typically includesan electronic circuit configured to perform the controlling operations.Control unit 340 preferably communicates with a data processor 154 whichtransmits digital data pertaining to fabrication instructions based oncomputer object data, e.g., a CAD configuration represented on acomputer readable medium in a form of a Standard Tessellation Language(STL) format or the like. Typically, control unit 340 controls thevoltage applied to each dispensing head or nozzle array and thetemperature of the building material formulation in the respectiveprinting head.

Once the manufacturing data is loaded to control unit 340 it can operatewithout user intervention. In some embodiments, control unit 340receives additional input from the operator, e.g., using data processor154 or using a user interface 116 communicating with unit 340. Userinterface 116 can be of any type known in the art, such as, but notlimited to, a keyboard, a touch screen and the like. For example,control unit 340 can receive, as additional input, one or more buildingmaterial formulation types and/or attributes, such as, but not limitedto, color, characteristic distortion and/or transition temperature,viscosity, electrical property, magnetic property. Other attributes andgroups of attributes are also contemplated.

Another representative and non-limiting example of a system 10 suitablefor AM of an object according to some embodiments of the presentinvention is illustrated in FIGS. 1B-1D. FIGS. 1B-1D illustrate a topview (FIG. 1B), a side view (FIG. 1C) and an isometric view (FIG. 1D) ofsystem 10.

In the present embodiments, system 10 comprises a tray 12 and aplurality of inkjet printing heads 16, each having a plurality ofseparated nozzles. Tray 12 can have a shape of a disk or it can beannular. Non-round shapes are also contemplated, provided they can berotated about a vertical axis.

Tray 12 and heads 16 are optionally and preferably mounted such as toallow a relative rotary motion between tray 12 and heads 16. This can beachieved by (i) configuring tray 12 to rotate about a vertical axis 14relative to heads 16, (ii) configuring heads 16 to rotate about verticalaxis 14 relative to tray 12, or (iii) configuring both tray 12 and heads16 to rotate about vertical axis 14 but at different rotation velocities(e.g., rotation at opposite direction). While the embodiments below aredescribed with a particular emphasis to configuration (i) wherein thetray is a rotary tray that is configured to rotate about vertical axis14 relative to heads 16, it is to be understood that the presentapplication contemplates also configurations (ii) and (iii). Any one ofthe embodiments described herein can be adjusted to be applicable to anyof configurations (ii) and (iii), and one of ordinary skills in the art,provided with the details described herein, would know how to make suchadjustment.

In the following description, a direction parallel to tray 12 andpointing outwardly from axis 14 is referred to as the radial directionr, a direction parallel to tray 12 and perpendicular to the radialdirection r is referred to herein as the azimuthal direction φ, and adirection perpendicular to tray 12 is referred to herein is the verticaldirection z.

The term “radial position,” as used herein, refers to a position on orabove tray 12 at a specific distance from axis 14. When the term is usedin connection to a printing head, the term refers to a position of thehead which is at specific distance from axis 14. When the term is usedin connection to a point on tray 12, the term corresponds to any pointthat belongs to a locus of points that is a circle whose radius is thespecific distance from axis 14 and whose center is at axis 14.

The term “azimuthal position,” as used herein, refers to a position onor above tray 12 at a specific azimuthal angle relative to apredetermined reference point. Thus, radial position refers to any pointthat belongs to a locus of points that is a straight line forming thespecific azimuthal angle relative to the reference point.

The term “vertical position,” as used herein, refers to a position overa plane that intersect the vertical axis 14 at a specific point.

Tray 12 serves as a supporting structure for three-dimensional printing.The working area on which one or objects are printed is typically, butnot necessarily, smaller than the total area of tray 12. In someembodiments of the present invention the working area is annular. Theworking area is shown at 26. In some embodiments of the presentinvention tray 12 rotates continuously in the same direction throughoutthe formation of object, and in some embodiments of the presentinvention tray reverses the direction of rotation at least once (e.g.,in an oscillatory manner) during the formation of the object. Tray 12 isoptionally and preferably removable. Removing tray 12 can be formaintenance of system 10, or, if desired, for replacing the tray beforeprinting a new object. In some embodiments of the present inventionsystem 10 is provided with one or more different replacement trays(e.g., a kit of replacement trays), wherein two or more trays aredesignated for different types of objects (e.g., different weights)different operation modes (e.g., different rotation speeds), etc. Thereplacement of tray 12 can be manual or automatic, as desired. Whenautomatic replacement is employed, system 10 comprises a trayreplacement device 36 configured for removing tray 12 from its positionbelow heads 16 and replacing it by a replacement tray (not shown). Inthe representative illustration of FIG. 1B tray replacement device 36 isillustrated as a drive 38 with a movable arm 40 configured to pull tray12, but other types of tray replacement devices are also contemplated.

Exemplified embodiments for the printing head 16 are illustrated inFIGS. 2A-2C. These embodiments can be employed for any of the AM systemsdescribed above, including, without limitation, system 110 and system10.

FIGS. 2A-2B illustrate a printing head 16 with one (FIG. 2A) and two(FIG. 2B) nozzle arrays 22. The nozzles in the array are preferablyaligned linearly, along a straight line. In embodiments in which aparticular printing head has two or more linear nozzle arrays, thenozzle arrays are optionally and preferably can be parallel to eachother.

When a system similar to system 110 is employed, all printing heads 16are optionally and preferably oriented along the indexing direction withtheir positions along the scanning direction being offset to oneanother.

When a system similar to system 10 is employed, all printing heads 16are optionally and preferably oriented radially (parallel to the radialdirection) with their azimuthal positions being offset to one another.Thus, in these embodiments, the nozzle arrays of different printingheads are not parallel to each other but are rather at an angle to eachother, which angle being approximately equal to the azimuthal offsetbetween the respective heads. For example, one head can be orientedradially and positioned at azimuthal position φ₁, and another head canbe oriented radially and positioned at azimuthal position φ₂. In thisexample, the azimuthal offset between the two heads is φ₁-φ₂, and theangle between the linear nozzle arrays of the two heads is also φ₁-φ₂.

In some embodiments, two or more printing heads can be assembled to ablock of printing heads, in which case the printing heads of the blockare typically parallel to each other. A block including several inkjetprinting heads 16 a, 16 b, 16 c is illustrated in FIG. 2C.

In some embodiments, system 10 comprises a support structure 30positioned below heads 16 such that tray 12 is between support structure30 and heads 16. Support structure 30 may serve for preventing orreducing vibrations of tray 12 that may occur while inkjet printingheads 16 operate. In configurations in which printing heads 16 rotateabout axis 14, support structure 30 preferably also rotates such thatsupport structure 30 is always directly below heads 16 (with tray 12between heads 16 and tray 12).

Tray 12 and/or printing heads 16 is optionally and preferably configuredto move along the vertical direction z, parallel to vertical axis 14 soas to vary the vertical distance between tray 12 and printing heads 16.In configurations in which the vertical distance is varied by movingtray 12 along the vertical direction, support structure 30 preferablyalso moves vertically together with tray 12. In configurations in whichthe vertical distance is varied by heads 16 along the verticaldirection, while maintaining the vertical position of tray 12 fixed,support structure 30 is also maintained at a fixed vertical position.

The vertical motion can be established by a vertical drive 28. Once alayer is completed, the vertical distance between tray 12 and heads 16can be increased (e.g., tray 12 is lowered relative to heads 16) by apredetermined vertical step, according to the desired thickness of thelayer subsequently to be printed. The procedure is repeated to form athree-dimensional object in a layerwise manner.

The operation of inkjet printing heads 16 and optionally and preferablyalso of one or more other components of system 10, e.g., the motion oftray 12, are controlled by a controller 20. The controller can have anelectronic circuit and a non-volatile memory medium readable by thecircuit, wherein the memory medium stores program instructions which,when read by the circuit, cause the circuit to perform controloperations as further detailed below.

Controller 20 can also communicate with a host computer 24 whichtransmits digital data pertaining to fabrication instructions based oncomputer object data, e.g., in a form of a Standard TessellationLanguage (STL) or a StereoLithography Contour (SLC) format, VirtualReality Modeling Language (VRML), Additive Manufacturing File (AMF)format, Drawing Exchange Format (DXF), Polygon File Format (PLY) or anyother format suitable for Computer-Aided Design (CAD). The object dataformats are typically structured according to a Cartesian system ofcoordinates. In these cases, computer 24 preferably executes a procedurefor transforming the coordinates of each slice in the computer objectdata from a Cartesian system of coordinates into a polar system ofcoordinates. Computer 24 optionally and preferably transmits thefabrication instructions in terms of the transformed system ofcoordinates. Alternatively, computer 24 can transmit the fabricationinstructions in terms of the original system of coordinates as providedby the computer object data, in which case the transformation ofcoordinates is executed by the circuit of controller 20.

The transformation of coordinates allows three-dimensional printing overa rotating tray. In conventional three-dimensional printing, theprinting heads reciprocally move above a stationary tray along straightlines. In such conventional systems, the printing resolution is the sameat any point over the tray, provided the dispensing rates of the headsare uniform. Unlike conventional three-dimensional printing, not all thenozzles of the head points cover the same distance over tray 12 duringat the same time. The transformation of coordinates is optionally andpreferably executed so as to ensure equal amounts of excess materialformulation at different radial positions. Representative examples ofcoordinate transformations according to some embodiments of the presentinvention are provided in FIGS. 3A-3B, showing three slices of an object(each slice corresponds to fabrication instructions of a different layerof the objects), where FIG. 3A illustrates a slice in a Cartesian systemof coordinates and FIG. 3B illustrates the same slice following anapplication of a transformation of coordinates procedure to therespective slice.

Typically, controller 20 controls the voltage applied to the respectivecomponent of the system 10 based on the fabrication instructions andbased on the stored program instructions as described below.

Generally, controller 20 controls printing heads 16 to dispense, duringthe rotation of tray 12, droplets of building material formulation inlayers, such as to print a three-dimensional object on tray 12.

System 10 optionally and preferably comprises one or more radiationsources 18, which can be, for example, an ultraviolet or visible orinfrared lamp, or other sources of electromagnetic radiation, orelectron beam source, depending on the modeling material formulationbeing used. Radiation source can include any type of radiation emittingdevice, including, without limitation, light emitting diode (LED),digital light processing (DLP) system, resistive lamp and the like.Radiation source 18 serves for curing or solidifying the modelingmaterial formulation. In various exemplary embodiments of the inventionthe operation of radiation source 18 is controlled by controller 20which may activate and deactivate radiation source 18 and may optionallyalso control the amount of radiation generated by radiation source 18.

In some embodiments of the invention, system 10 further comprises one ormore leveling devices 32 which can be manufactured as a roller or ablade. Leveling device 32 serves to straighten the newly formed layerprior to the formation of the successive layer thereon. In someembodiments, leveling device 32 has the shape of a conical rollerpositioned such that its symmetry axis 34 is tilted relative to thesurface of tray 12 and its surface is parallel to the surface of thetray. This embodiment is illustrated in the side view of system 10 (FIG.1C).

The conical roller can have the shape of a cone or a conical frustum.

The opening angle of the conical roller is preferably selected such thatis a constant ratio between the radius of the cone at any location alongits axis 34 and the distance between that location and axis 14. Thisembodiment allows roller 32 to efficiently level the layers, since whilethe roller rotates, any point p on the surface of the roller has alinear velocity which is proportional (e.g., the same) to the linearvelocity of the tray at a point vertically beneath point p. In someembodiments, the roller has a shape of a conical frustum having a heighth, a radius R₁ at its closest distance from axis 14, and a radius R₂ atits farthest distance from axis 14, wherein the parameters h, R₁ and R₂satisfy the relation R₁/R₂=(R−h)/h and wherein R is the farthestdistance of the roller from axis 14 (for example, R can be the radius oftray 12).

The operation of leveling device 32 is optionally and preferablycontrolled by controller which may activate and deactivate levelingdevice 32 and may optionally also control its position along a verticaldirection (parallel to axis 14) and/or a radial direction (parallel totray 12 and pointing toward or away from axis 14.

In some embodiments of the present invention system 10 comprises coolingsystem (not shown, see FIG. 1A) such as one or more fans or the like.

In some embodiments of the present invention printing heads 16 areconfigured to reciprocally move relative to tray along the radialdirection r. These embodiments are useful when the lengths of the nozzlearrays 22 of heads 16 are shorter than the width along the radialdirection of the working area 26 on tray 12. The motion of heads 16along the radial direction is optionally and preferably controlled bycontroller 20.

Some embodiments contemplate the fabrication of an object by dispensingdifferent building material formulations from different dispensingheads. These embodiments provide, inter alia, the ability to selectmaterial formulations from a given number of material formulations anddefine desired combinations of the selected material formulations andtheir properties. According to the present embodiments, the spatiallocations of the deposition of each building material formulation withthe layer is defined, either to effect occupation of differentthree-dimensional spatial locations by different building materialformulations, or to effect occupation of substantially the samethree-dimensional location or adjacent three-dimensional locations bytwo or more different material formulations so as to allow postdeposition spatial combination of the material formulations within thelayer, thereby to form a composite material formulation at therespective location or locations.

Any post deposition combination or mix of building material formulationsis contemplated. For example, once a certain modeling materialformulation is dispensed it may preserve its original properties.However, when it is dispensed simultaneously with another modelingmaterial formulation or other dispensed material formulations which aredispensed at the same or nearby locations, a composite materialformulation having a different property or properties to the dispensedmodeling material formulations is formed.

The present embodiments thus enable the deposition of a broad range ofmaterial formulation combinations, and the fabrication of an objectwhich may consist of multiple different combinations of materialformulations, in different parts of the object, according to theproperties desired to characterize each part of the object.

Further details on the principles and operations of an AM systemsuitable for the present embodiments are found in U.S. PublishedApplication No. 20100191360, the contents of which are herebyincorporated by reference.

FIG. 4 is a schematic illustration of a tubular structure 200 accordingto some embodiments of the present invention. Tubular structure 200 ispreferably fabricated by AM (for example, by operating one of AM systems10 and 110) from non-biological building material formulations. Invarious exemplary embodiments of the invention tubular structure 200 hasa shape, and optionally and preferably also mechanical properties, of ablood vessel. Tubular structure 200 can comprise an elongated core 202and a solid shell 204 encapsulating core 202.

In some embodiments, the smallest dimension of shell 204 (e.g., itsouter diameter) is, from about 0.1 mm to about 5 cm, or from about 1 mmto about 3 cm. In some embodiments, the wall thickness of shell 204 isfrom about 0.1 mm to about 5 mm, or from about 0.1 mm to about 3 mm.

Core 202 is optionally and preferably sacrificial. In some optional andpreferred embodiments, tubular structure 200 also comprises anintermediate shell 206 between core 202 and shell 204. Intermediateshell is optionally and preferably also sacrificial. Each of core 202,shell 204 and intermediate shell 206 is optionally and preferably madeof a different material or a different combination of materials.

In some embodiments of the present invention, core 202 is made of aliquid or liquid-like material, as defined herein (e.g., Material L).When core 202 is made of a liquid or liquid-like material and tubularstructure 200 comprises also intermediate shell 206, the intermediateshell 206 is preferably made of a gel or gel-like material, as describedherein (e.g., Material S). The inventors found that such intermediateshell 206 significantly reduces the likelihood of inward collapse. Theintermediate shell 206 serves as a buffer layer between the core 202 andthe outer shell 204, and optionally and preferably prevents contactbetween the liquid or liquid-like core and the solid shell. The liquidor liquid-like core can be removed, for example, by application ofpressure inside the structure 200. The pressure is preferably no morethan 1 bar, or no more than 0.5, or no more than 0.3 bar, and can be,for example, 0.1 bar, 0.2 bar, or 0.3 bar.

Following the removal of core 202, the intermediate shell 206, ifexists, typically remains in tubular structure 200. The intermediateshell 206 can then be removed by circulating in tubular structure 200 asolution capable of dissolving or dispersing the intermediate shell 206.For example, intermediate shell 206 can be made of a hardened supportmaterial (e.g., Material S) that is water-soluble or water-miscible, inwhich intermediate shell 206 can be removed by contacting an aqueoussolution at which it is dissolvable or dispersible (e.g., a cleaningsolution; an aqueous solution that comprises an alkaline substance, atan amount of about 1% to about 3% by weight of the solution). In someembodiments, intermediate shell 206 is removed upon applying physicalmeans such as an air or liquid jet at a pressure higher than 0.5 bar orhigher than 1 bar. This pressure is optionally and preferably higherthan the pressure used for removing core 202.

The dimensions of core 202 and intermediate shell 206 are optionally andpreferably selected based on the desired inner diameter of shell 204 oftubular structure 200. FIG. 5 illustrates parameters that can be usedaccording to some embodiments of the present invention forcharacterizing the dimensions of core 202 and intermediate shell 206.Shown are a maximal core diameter parameter L_(MAX), a minimal thicknessof the intermediate layer parameter c_(MIN), and two thresholds diameterparameters D₁ and D₂.

L_(MAX) is typically, but not necessarily, less than 10 mm, and c_(MIN)is typically, but not necessarily less than 20 mm and more than 0.4 mmor less than 2 mm and more than 0.4 mm. The thresholds D₁ and D₂ areoptionally and preferably calculated based on L_(MAX) and c_(MIN) andthe vessel geometry. For example, D₁ can be calculated as a linearcombination of L_(MAX) and c_(MIN), e.g., D₁=L_(MAX)+2*K₁*c_(MIN), whereK₁ is larger than 1 and typically from about 2 to about 5. D₂ can becalculated as a linear function of Lmax, e.g., D₂=L_(MAX)*K₂ where K₂ istypically from 0.8 to about 1.2. In some embodiments of the presentinvention the ratio between the coefficients K₂ and K₁ is less than4c_(MIN) or less than 3c_(MIN) or less than 2c_(MIN).

In some embodiments of the present invention in regions of tubularstructure 200 in which the inner diameter of the outer shell 204 islarger than or equals to the first threshold diameter D₁, the diameterof core 202 preferably has a generally constant diameter, for example,the same as the L_(MAX) parameter. In some embodiments of the presentinvention, in regions of tubular structure 200 in which the innerdiameter of the outer shell 204 is less than or equals to the secondthreshold diameter D₂, the thickness of the intermediate shell 206(along a radial direction perpendicular to the longitudinal axis of thetube) is preferably generally constant, for example, the same as thec_(MIN) parameter. In some embodiments of the present invention, inregions of the tubular structure in which the inner diameter of theouter shell 204 is between the second threshold diameter D₂ and thefirst threshold diameter D₁, the diameter of the core 202 is less thanL_(MAX) and the thickness of the intermediate shell 206 is more thanc_(MIN). In these regions, the diameter of core 202 and the thickness ofintermediate shell 206 are not necessarily constant along tubularstructure 200. For example, when tubular structure includes regions inwhich the inner diameter of outer shell 204 varies, the diameter of core202 and the thickness of intermediate shell 206 can vary reciprocally sothat an increment in the diameter of core 202 is accompanied by adecrement of the thickness of intermediate shell 206. The variation ofthe diameter of the core and the thickness of the intermediate shell isoptionally and preferably monotonic, e.g., a linear variation.

The present embodiments also contemplate a configuration in which core202 is made of a gel or gel-like material, as defined herein (e.g.,Material S), and intermediate shell 206 is made of a liquid orliquid-like material, as defined herein (e.g., Material L). Theadvantage of these embodiments is that the non-solid intermediate shell206 reduces friction between core 202 and shell 204 and thereforfacilitates easy removal of core 202 from tubular structure 202, whilereducing or eliminating the need to circulate a solution in for theremoval. Another advantage is that a gel or gel-like core can provide abetter support against an inward collapse.

The gel or gel-like material forming core 202 (in embodiments in whichcore 202 is gel or gel-like material) or intermediate shell 206 (inembodiments in which intermediate shell 206 is gel or gel-like material)can be any building material, preferably a support material, suitablefor use in AM. For example, a gel or gel-like material can be a buildingmaterial having a modulus of elasticity of from about 0.05 MPa to about0.5 MPa according to ASTM D-575, or from about 0.1 MPa to about 1 MPaaccording to ASTM D-575, and/or feature any of the properties describedherein for a gel or gel-like material such as Material S.

The gel or gel-like material can be obtained in some embodiments of thepresent invention by dispensing a curable support material formulationor a combination of two or more curable support material formulations(for example, to form a digital material as described herein), or acombination of at least one curable support material formulation and atleast one curable modeling material formulation (for example, to form adigital material as described herein).

The gel or gel-like materials can be obtained, in some embodiments ofthe present invention using any of the known curable formulations thatprovide, when exposed to a curing condition as described herein, ahardened support material as known in the art as usable in the contextof these embodiments, typically formulations that provide, whenhardened, a material that is water-soluble or water-miscible orwater-breakable, and/or which is removal by physical means (e.g., waterjet) or chemical means (e.g., a cleaning solution) as known in the art.

According to embodiments, the curable support material formulationprovides, upon exposure to a curing condition, a hardened, gel orgel-like support material featuring at least one of:

-   -   a Shear loss modulus G″ to Shear storage modulus G′ ratio (tan        delta) that is lower than 1;    -   flowability and/or breakability when subjected to a liquid        pressure higher than 0.5 bar or higher than 1 bar; and    -   water-solubility or water-immiscibility, as defined herein.

Such a curable support material is also referred to herein asFormulation S.

Exemplary curable support material formulations S include one or morecurable materials, preferably hydrophilic or amphiphilic curablematerials, such as, for example, described herein in Example 1, furtherpreferably mono-functional curable materials; one or more non-curablematerials, preferably hydrophilic or amphiphilic polymeric materials,such as, for example, described herein in Example 1, and one or moreinitiators, for promoting the hardening of the curable materials.

Exemplary support material formulations include, but are not limited,those marketed as SUP705, SUP706 and SUP707. The hardened gel orgel-like materials obtained upon exposing these formulations to a curingcondition (typically UV radiation) can be removed using cleaningsolutions and/or physical means as recommended for these formulations.

The liquid or liquid-like material is a building material that featuresproperties that are substantially the same, or resemble, propertiescharacterizing a liquid.

Herein throughout and in the art, the term “liquid” describes a fluidthat does not change its volume in response to stress. Liquid materialsare characterized by fluidity, that is, the ability to flow as themolecules move by passing one by another; a viscosity, that is, aresistance to shear stress; by very low or zero shear modulus (G); andby a shear loss modulus to shear storage modulus ratio (G″/G′, or tandelta) higher than 1, typically higher than 10.

Herein, a “liquid-like material” describes a gel-like or paste-likematerial that features properties similar to those of a liquid, byfeaturing, for example, a low shear modulus, e.g., lower than 100 kPa orlower than 50 kPa or lower than 10 kPa; and/or by a shear loss modulusto shear storage modulus ratio (tan θ) higher than 1, or by shearthinning behavior and hence its fluidity, viscosity and flowabilityresemble those of a liquid.

In some embodiments of the present invention, liquid and liquid-likematerials feature one or more of the following characteristics:

-   -   a viscosity of no more than 10000 centipoises; and/or    -   Shear loss modulus to Shear storage modulus ratio (tan delta)        greater than 1; and/or    -   Shear-thinning and/or thixotropic behavior; and/or    -   Thermal-thinning behavior; and/or    -   a Shear storage modulus lower than 20 kPa; and/or    -   flowability when subjected to a positive pressure lower than 1        bar or lower than 0.5 bar.

Such materials are collectively referred to herein as Material L.

Shear storage modulus, G′, is also referred to herein interchangeably as“storage shear modulus”, and reflects an elastic behavior of a material.Liquid materials are typically non-elastic and hence feature a low shearstorage modulus.

Shear loss modulus, G″, is also referred to herein interchangeably as“loss shear modulus”, and reflects a viscous behavior of a material.

Storage shear modulus and loss shear modulus may optionally bedetermined using a shear rheometer, for example, a strain-controlledrotational rheometer, at an indicated temperature and frequency (e.g.,using procedures well known in the art).

The Shear loss modulus to Shear storage modulus ratio, G″/G′, also knownas “tan delta”, reflects the viscoelastic behavior of a material. Liquidmaterials are typically more viscous and non-elastic and hence forliquids or liquid-like materials this ratio is higher than 1. Gels aretypically elastic and hence this ratio for gel or gel-like materials islower than 1.

Herein throughout, the term “shear-thinning” describes a property of afluidic compound or a material that that is reflected by a decrease inits viscosity (increase in its fluidity) upon application of shearforces (under shear strain). In some of the present embodiments, ashear-thinning material is such that exhibits a significant, e.g., atleast 100%, reduction in its Shear modulus upon increasing the shearstrain from about 1% to above 50%.

Herein throughout, the term “thixotropic” describes a property of afluidic compound or material that is reflected by a time-dependentshear-thinning, that is its viscosity is decreased in correlation withthe time at which shear forces are applied, and returns back to itsoriginal value when application of shear forces is ceased. In some ofthe present embodiments, a thixotropic material is such that exhibits asignificant, e.g., at least 100%, reduction in its Shear modulus under50% strain.

Herein throughout, the term “thermal-thinning” describes a property of afluidic compound or a material that is reflected by a decrease in itsviscosity (increase in its fluidity) upon application of heat energy(increase in temperature). In some of the present embodiments,thermal-thinning materials feature a decrease in viscosity or shearmodulus by at least 20%, or at least 50%, or even 100%, upon beingheated to a temperature of from 40 to 95° C., including any intermediatevalue and subranges therebetween.

Example 2 in the Examples section that follows describes an exemplarybuilding material formulation usable for providing a liquid orliquid-like material as described herein. Such a formulation is alsoreferred to herein as “liquid formulation” or as “formulation L”.

The one or more modeling material formulations comprise one or morecurable materials, optionally in combination with one or morenon-curable materials and further optionally in combination with aninitiator, surface active agents, impact modifiers, coloring agents,thickening agents, and the like.

Preferably the one or more modeling material formulations comprisecurable materials in an amount of at least 50% by weight of the totalweight of the modeling material formulations.

In some embodiments, the curable materials are UV-curable materials andthe formulations further comprise one or more photoinitiators.

In some embodiments, the UV-curable materials are acrylate ormethacrylates, and can include monomeric, oligomeric or polymericacrylates and/or methacrylates.

The modeling material formulations are such that upon exposure to acuring condition (e.g., UV irradiation), the curable materialpolymerizes, providing a hardened (cured; solidified) material, or aplurality of hardened materials (e.g., digital materials).

The components of the modeling material formulations and the dispensingthereof are dictated by the desired properties of the final object.

Shell 204 can be made of any modeling material or combination ofmodeling materials known in the art. The material forming shell 204 canbe obtained in some embodiments of the present invention by dispensing acurable modeling material formulation or a combination of two or morecurable modeling material formulations (for example, to form a digitalmaterial as described herein), or a combination of at least one curablesupport material formulation and at least one curable modeling materialformulation (for example, to form a digital material as describedherein). In various exemplary embodiments of the invention at least oneof the materials forming shell 204 has a zero (0) or close to zero(e.g., 10 or less, or 5 or less) Shore A hardness, or a Shore 00hardness lower than 30. A representative example of such a material,which is suitable for shell 204 is described in Example 1, below.

The material forming shell 204 can be a digital material combining amaterial formulation C₁ and material formulation C₂, wherein C₁ can havea tensile strength of from about 2 to about 4 MPa according to ASTMD-412 and a Shore A hardness from about 25 MPa to about 35 MPa accordingto ASTM D-224D and C₂ can have has a tensile strength of from about 20MPa to about 40 MPa MPa according to ASTM D-638-03 and a modulus ofelasticity of from about 750 MPa MPa to about 1500 MPa MPa according toASTM D-638-04.

FIG. 6 is a schematic illustration of tubular structure 200 inembodiments in which shell 204 is embedded in a supporting structure208. Supporting structure 208 can have any shape and is preferablyencapsulate shell 204 around its periphery, optionally and preferablyleaving one or two stems 204 a and 204 b of tubular structure 200protruding outside supporting structure 208. The advantage of havingsupporting structure 208 is that it facilitates handling andtransporting. An additional advantage is that the encapsulation protectsthe shell 204 during the process of removing the sacrificial core 202and, if present, the sacrificial intermediate shell 206. Theseembodiments are particularly useful when shell 204 is soft, e.g., madeof the material described in Example 1, below. These embodiments arealso useful when shell 204 has a low wall thickness (e.g., wallthickness less than 0.5 mm) and low outer diameter (e.g., less than 10mm).

In various exemplary embodiments of the invention supporting structure208 is sacrificial. For example, supporting structure 208 can be made ofa support material. In these embodiments, following the removal of thecore 204 and, if exists, the intermediate shell 206, and optionally alsofollowing the handling and/or transportation of tubular structure 200,supporting structure 208 is removed, for example, using any knowntechnique for removing AM support materials.

FIGS. 7A-7C are schematic illustrations of tubular structure 200 inembodiments of the invention in which tubular structure 200 comprisesreinforcing elements 201 embedded in shell 204. Reinforcing elements 210are optionally and preferably oriented to effect anisotropic mechanicalproperties of shell 204. This is advantageous for mimicking bloodvessels which are known to have different mechanical properties inresponse to radially applied forces than in response to longitudinallyapplied forces. FIG. 7A illustrates an embodiment in which reinforcingelements 210 comprise elongated reinforcing elements embedded in shell204 parallel to a longitudinal axis 212 of shell, FIG. 7B illustrates anembodiment in which reinforcing elements 210 comprise annularreinforcing elements embedded in shell along an azimuthal direction 214defining shell 204, and FIG. 7C illustrates an embodiment in whichreinforcing elements 210 comprise both annular reinforcing elementsalong azimuthal direction 214 and elongated reinforcing elementsparallel to longitudinal axis 212.

Reinforcing elements 210 are optionally and preferably made of amaterial having a hardness level that is higher than the material ofshell 204. A suitable material for reinforcing elements 210 can have atensile strength of from about 2 to about 4 MPa according to ASTM D-412and a Shore A hardness from about 25 MPa to about 35 MPa according toASTM D-224D. For example, reinforcing elements 210 can be made ofrubber-like materials usable in PolyJet™ systems, for example, materialsmarketed under the trade name “Agilus™” family, e.g., Agilus™30) whichutilizes an elastomeric curable material, and optionally silicaparticles. Exemplary such materials are described in PCT InternationalApplication No. IL2017/050604 (Published as WO2017/208238), by thepresent assignee, the contents of which are hereby incorporated byreference. Additional exemplary families of Rubber-like materials usablein PolyJet™ systems include those marketed under the trade names“Tango™” the “Tango+™”, which offer a variety of elastomercharacteristics of the obtained hardened material, including Shore Ahardness, Elongation at break, Tear Resistance and Tensile strength.Exemplary curable elastomeric formulations usable for forming suchrubbery-like materials are also described in Example 3, below.

FIG. 8 is a schematic illustration of tubular structure 200 in acut-open view, in embodiments of the invention in which tubularstructure 200 comprises a liner layer 216 at least partially coating aninner surface 218 of shell 204. Liner layer 216 is preferably betweenintermediate shell 206 and inner surface 208, however, for clarity ofpresentation, intermediate shell 206 is not illustrated in FIG. 8 .Liner layer 216 can be made of any building material suitable for AM.Liner layer 216 can be made of any building material. In someembodiments of the present invention liner layer 216 can be made of amaterial having a zero (0) or close to zero (e.g., 10 or less, or 5 orless) Shore A hardness, or a Shore 00 hardness lower than 40.Representative example of such a material is provided in Example 1below. Alternatively, liner layer 216 can be made of a support material,e.g., a material having a modulus of elasticity of from about 10 kPa toabout 100 kPa or from about 10 kPa to about 50 kPa or from about 0.1 MPato about 1 MPa according to ASTM D-575 (Material S as described hereinbeing an exemplary support material), optionally and preferably coatedwith an elastomeric curable material, e.g., a material having have atensile strength of from about 2 to about 4 MPa according to ASTM D-412and a Shore A hardness from about 25 MPa to about 35 MPa according toASTM D-224D. Representative example of such a suitable elastomericcurable material is provided in Example 3 below. Still alternatively,the liner layer 216 can be of combination of two or more of thesematerials, e.g., a digital material combination as further detailedhereinbelow.

In various exemplary embodiments of the invention the attachment betweenliner layer 216 and shell 204 is stronger than the attachment betweenintermediate shell 206 and liner layer 216. These embodiments are usefulwhen it is desired to remove intermediate shell 206 without removingliner layer 216. When intermediate shell 206 is made of a gel orgel-like material (e.g., Material S), the circulation of solution intubular structure 200 for the removal of intermediate shell 206 isoptionally and preferably at flow rates that are sufficiently low so asnot remove liner layer 216. When intermediate shell 206 is made of aliquid or liquid-like material (e.g., Material L), the extraction ofcore 202 and intermediate shell 206 is optionally and preferably atsufficiently low forces so as not remove liner layer 216. In someembodiments of the present invention liner layer 216 is harder thanshell 204. Optionally and preferably the material and/or texture ofliner layer 216 is selected such that liner layer 216 has mechanicalproperties of plaque tis sue.

FIG. 25 is a schematic illustration of an object 230 fabricated byadditive manufacturing from non-biological building materialformulations. The object 230 has a shape of an organ, and preferablycomprises one or more structures having a shape of a blood vessel, e.g.,tubular structure 200, and one or more structures 232 having a shape ofa bodily structure other than a blood vessel. For example, structure 232can have a shape of a brain, a head, a limb, a neck, a heart, a lung, aliver, a pancreas, a spleen, a thymus, an esophagus, a stomach, anintestine, a kidney, a testis, an ovary, a bone, a breast, an uterus, abladder, a spinal cord, an eye, an ear or the like

FIG. 26 is an image of an interconnected network 240 of elongatedstructures, fabricated according to some embodiments of the presentinvention by additive manufacturing from non-biological buildingmaterial formulations. Each elongated structure has a shape of a bloodvessel and can be, for example, tubular structure 200. In someembodiments of the present invention interconnected network 240comprises one or more support jigs 242 configured for maintaininginterconnected network 240 in a three-dimensional arrangement.

FIG. 27 is a flowchart diagram of a method of additive manufacturing ofat least one tubular structure featuring properties of a blood vessel,according to some embodiments of the present invention. The methodbegins at 270 and optionally and preferably proceeds to 271 at whichcomputer object data in any of the aforementioned formats are obtained.An exemplified technique for obtaining the computer object data isdescribed hereinunder with reference to FIGS. 28A and 28B.

The method can proceed to 272 at which a layer of one or more buildingmaterial formulation(s) is dispensed. The building material formulationcan be a modeling material formulation and/or a support materialformulation and/or a formulation providing a liquid or liquid-likematerial when exposed to a curing condition, as described herein. Insome embodiments of the present invention the method selectivelydispenses for a particular layer, one or more regions of modelingmaterial formulations and one or more regions of support materialformulation and/or a formulation providing a liquid or liquid-likematerial when exposed to a curing condition, as described herein. Themodeling material formulation is preferably dispensed in a configuredpattern corresponding to the shape of the object and in accordance withthe computer object data. The other building material formulations arepreferably dispensed in accordance with the computer object data, butnot necessarily in accordance with the shape of the object, since thesebuilding material formulations are typically sacrificial.

Optionally, before being dispensed, the uncured building material, or apart thereof (e.g., one or more formulations of the building material),is heated, prior to being dispensed. These embodiments are particularlyuseful for uncured building material formulations having relatively highviscosity at the operation temperature of the working chamber of a 3Dinkjet printing system. The heating of the formulation(s) is preferablyto a temperature that allows jetting the respective formulation througha nozzle of a printing head of a 3D inkjet printing system. In someembodiments of the present invention, the heating is to a temperature atwhich the respective formulation exhibits a viscosity of no more than Xcentipoises, where X is about 30 centipoises, preferably about 25centipoises and more preferably about 20 centipoises, or 18 centipoises,or 16 centipoises, or 14 centipoises, or 12 centipoises, or 10centipoises, or even lower.

The heating can be executed before loading the respective formulationinto the printing head of the AM (e.g., 3D inkjet printing) system, orwhile the formulation is in the printing head or while the compositionpasses through the nozzle of the printing head.

In some embodiments, the heating is executed before loading of therespective formulation into the dispensing (e.g., inkjet printing) head,so as to avoid clogging of the dispensing (e.g., inkjet printing) headby the formulation in case its viscosity is too high.

In some embodiments, the heating is executed by heating the dispensing(e.g., inkjet printing) heads, at least while passing the modelingmaterial formulation(s) through the nozzle of the dispensing (e.g.,inkjet printing) head.

In some embodiments, during the dispensing of a material formulationthat is to remain in a liquid or liquid-like in the final object (e.g.,formulation L) the operation of the cooling system described below istemporarily terminated, so as to maintain a still-air environment.

As used herein, “still-air environment” refers to an environment inwhich there is no air flow, or in which an air flows at speed less than3 m/s.

At 273 the newly dispensed layer is straightened, for example, using aleveling device 32 or 132, which is optionally and preferably rotatable.When the newly dispensed layer contains a material formulation that isto remain in a liquid or liquid-like in the final object (e.g.,Formulation L), the rotation speed of the leveling device is preferablychanged, typically reduced, relative to its speed when straighteningother layers. The control over the rotation speed of the leveling devicecan be done by a controller (e.g., controller 20 or controller 340).

The method optionally and preferably proceeds to 274 at which thedeposited layer is exposed to a curing condition (e.g., curing energy isapplied), e.g., by means of a hardening device, for example, a radiationsource as described herein. Preferably, the curing is applied to eachindividual layer following the deposition of the layer and prior to thedeposition of the previous layer. Optionally, the deposited (dispensed)layers are exposed to the curing condition other than a curing energy,such as, but not limited to, contact with a chemical reagent or exposureto the environment.

Operations 272-274, and in some embodiments also 271, are preferablyexecuted sequentially a plurality of times so that a plurality of layersare sequentially dispensed and solidified. This is illustrated in FIG.27 as loop back arrows pointing from operation 274 to operations 271 and272. The layers are dispensed to form a stack of model layers made of amodeling material formulation, and a sacrificial structure, wherein thestack of model layers and the sacrificial structure are separable fromeach other in a manner that maintains the shape and size of the stack ofmodel layers without deformation. In various exemplary embodiments ofthe invention operations 272-274 are executed to so that the layers forman elongated core (e.g., core 202), and a shell (e.g., shell 204)encapsulating the core and having the shape of a blood vessel, whereinthe core is optionally and preferably the sacrificial structure. In someembodiments of the present invention these operations are executed alsoto form an intermediate shell (e.g., intermediate shell 206) between thecore and the shell. Each of the core, the shell and the intermediateshell (when formed) is formed by dispensing a different buildingmaterial formulation or a different combination of building materialformulations. The core and the intermediate shell (when formed) areoptionally and preferably formed by dispensing a building material thatcan be removed after the object is completed, and are thereforesacrificial, as described herein.

Typically, a liquid or liquid-like material (e.g., Material L) is usedfor filling cavities less than 4 mm in width along their smallestdimension, and gel or gel-like support (e.g., Material S) or acombination of liquid or liquid-like and gel or gel-like materials forfilling cavities having width along their smallest dimension of morethan 4 mm. Preferably, when liquid or liquid-like or gel or gel-likematerial is dispensed and straightened, the AM system ensures, forexample, by means of controller 20 or 340, that the newly dispensedlayer is in a still-air environment.

In some embodiments of the present invention the method dispensesdigital material formulation for at least one of the layers.

The phrase “digital material formulations”, as used herein and in theart, describes a combination of two or more material formulations on amicroscopic scale or voxel level such that the printed zones of aspecific material formulation are at the level of few voxels, or at alevel of a voxel block. Such digital material formulations may exhibitnew properties that are affected by the selection of types of materialformulations and/or the ratio and relative spatial distribution of twoor more material formulations.

In exemplary digital material formulations, the modeling or supportmaterial formulation of each voxel or voxel block, obtained upon curing,is independent of the modeling or support material formulation of aneighboring voxel or voxel block, obtained upon curing, such that eachvoxel or voxel block may result in a different modeling or supportmaterial formulation and the new properties of the whole object are aresult of a spatial combination, on the voxel level, of severaldifferent model material formulations.

Herein throughout, whenever the expression “at the voxel level” is usedin the context of a different material formulation and/or properties, itis meant to include differences between voxel blocks, as well asdifferences between voxels or groups of few voxels. In preferredembodiments, the properties of the whole object are a result of aspatial combination, on the voxel block level, of several differentmodel material formulations.

In various exemplary embodiments of the invention operations 272-274 areexecuted to form, for at least a portion of layers, voxel elementscontaining different building material formulations at interlacedlocations.

In some embodiments, at least one, or at least a few (e.g., at least 10,at least 20, at least 30 at least 40, at least 50, at least 60, at least80, or more), of the layers is/are formed by dispensing droplets of twoor more building material formulations at interlaced locations, eachbuilding material formulation from a different dispensing (e.g., inkjetprinting) head. These building material formulations can include: (i)two or more modeling material formulations as described herein in any ofthe respective embodiments, (ii) at least one modeling materialformulation and at least one support material formulation (liquid,liquid-like or hardened) as described herein in any of the respectiveembodiments, or (iii) two or more support material formulations (liquid,liquid-like or hardened) as described herein in any of the respectiveembodiments.

The interlaced locations are optionally and preferably selected such asto form a 3D textured region spanning over these layers. The interlacedlocations are optionally and preferably selected according to amodulating function. The modulation function receives a position of acandidate voxel and provides an output value, which is then used toselect the material formulation for the candidate voxel. Thus, onebuilding material formulation is designated for the candidate voxel whenthe output value is within one predetermined range of output values,another building material formulation is designated for the candidatevoxel when the output value is within another predetermined range ofoutput values, and so on. Typically, there is at least one output valueor range of output values for which no material is designated for thecandidate voxel. The material designation for the candidate voxel isoutput for the AM system that dispenses the designated formulation atthe location of the candidate voxel.

In some embodiments of the present invention, distance fields areemployed in combination with the modulating function. Typically, a voxelis selected from a 3D build space and a distance field value relative tothe 3D object in the build space is determined for the selected voxel.The distance field value can then be used as an input for the modulatingfunction. Thus, in these embodiments, the modulating function receivesthe position and distance field value of the candidate voxel andprovides an output value, which is then used to select the buildingmaterial formulation for the candidate voxel as further detailedhereinabove.

The present embodiments contemplate many types of modulating functions.For example, in some embodiments of the present invention the modulatingfunction comprises a noise function. Representative examples of noisefunctions suitable for being included in the modulating functioninclude, without limitation, a simplex noise function, an open simplexnoise function, a Worley noise function, a Perlin noise function, awavelet noise function, and a value noise function. In some embodiments,the modulating function comprises a periodic function. Typically, butnot necessarily, the periodic modulating function has a period of 2 orless mm. In some embodiments, the modulating function comprises anaperiodic function. Combination of two or more of these or otherfunctions is also contemplated. A more detailed description of theconcept of modulating functions and distance fields is provided in theExamples section that follows (see Example 4).

In some embodiments, the method continues to 275, at which the liquid orliquid-like material (e.g., Material L) is removed from the printedobject, to thereby reveal the final object. The removal of the liquid orliquid-like material is optionally and preferably by application ofpressure, into a cavity or cavities filled by the liquid or liquid-likematerial. The pressure is optionally and preferably sufficient to effecta flow of the liquid or liquid-like material out of the cavity withoutcausing pressure induced damage to the shell or shells enclosing thecavity. Optionally, and preferably in case the liquid or liquid-likematerial features a thermal-thinning behavior, the object is heated, forexample, to a temperature of from about 40° C. to about 95° C. prior tothe removal of the liquid or liquid-like material.

When the removal of the liquid or liquid-like material is by applicationof pressure, the pressure can be, for example, an air pressure, or aliquid pressure, for example, in a form of a jet of an aqueous solution(e.g., water).

The pressure is preferably no more than 1 bar, or no more than 0.5, orno more than 0.3 bar, and can be, for example, 0.1 bar, 0.2 bar, or 0.3bar.

Alternatively, and optionally in addition to the above, and particularlyin cases where the liquid or liquid-like material is not sufficientlyflowable at ambient conditions, removing the liquid or liquid-likematerial is effected by applying a condition that renders the liquid orliquid-like material flowable. Such conditions include, for example,application of shear forces (for example, when the material to beremoved is a shear-thinning material), and/or application of a heatenergy (for example, when the material to be removed is athermo-thinning material).

Optionally and preferably hardened support structures formed by curablesupport material formulation or combination of curable supportformulation and other curable building formulations is also removed at275. When the hardened support structure forms the intermediate shell,its removal is optionally and preferably by circulating in the cavityoccupied by the intermediate shell a solution capable of removing thehardened support structure. For example, the gel or gel-like hardenedsupport structure can be water-soluble or water-miscible, in which caseit is removed by contacting an aqueous solution at which it isdissolvable or dispersible (e.g., a cleaning solution; an aqueoussolution that comprises an alkaline substance, at an amount of about 1%to about 3% by weight of the solution).

In some embodiments, the gel or gel-like support material is removedupon applying physical means such as an air or liquid jet at a pressurehigher than 0.5 bar or higher than 1 bar. This pressure is optionallyand preferably higher than the pressure used for removing the liquid orliquid-like material.

When the solid support structure forms the core, its removal can beeffected, optionally and preferably without circulating a solution, bypulling it out through an open end of the shell.

The method ends at 276.

FIG. 28A is a flowchart diagram of an exemplified procedure which can beused according to some embodiments of the present invention forexecuting operation 271 above. The procedure is particularly useful forobtaining computer object data for use with system 10 or system 110. Itis to be understood that, unless otherwise defined, the operationsdescribed hereinbelow can be executed either contemporaneously orsequentially in many combinations or orders of execution. Specifically,the ordering of the flowchart diagram is not to be considered aslimiting. For example, two or more operations, appearing in thefollowing description or in the flowchart diagrams in a particularorder, can be executed in a different order (e.g., a reverse order) orsubstantially contemporaneously. Additionally, several operationsdescribed below are optional and may not be executed.

The procedure begins at 700 and optionally and preferably continues to701 at which data in a format suitable for Digital Imaging andCommunications in Medicine (hereinafter DICOM data) are received.

The DICOM data can be received from an acquisition console such as, butnot limited to, an MRI system, a CT imaging system, a helical CT system,a positron emission tomography (PET) system, a 2D or 3D fluoroscopicimaging system, a 2D, 3D, or 4D ultrasound imaging system, an endoscopesystem, a bedside monitor system, an x-ray system, and a hybrid-imagingsystem capable of CT, MR, PET, ultrasound or other imaging techniques.The DICOM data preferably includes one or more digital image datadescribing one or more bodily structures comprising one or more tissueelements. In some embodiments of the present invention DICOM datapreferably includes one or more digital image data describing one ormore blood vessels, in some embodiments of the present invention DICOMdata includes one or more digital image data describing one or morebodily structures comprising one or more tissue elements other than ablood vessel, and in some embodiments of the present invention DICOMdata includes one or more digital image data describing one or moreblood vessels, and also one or more digital image data describing one ormore bodily structures comprising one or more tissue elements other thana blood vessel.

The procedure optionally and preferably continues to 702 at which theDICOM data are converted to computer object data. For instance, thecomputer object data can be in any known format, including, withoutlimitation, a Standard Tessellation Language (STL) or aStereoLithography Contour (SLC) format, Virtual Reality ModelingLanguage (VRML), Additive Manufacturing File (AMF) format, DrawingExchange Format (DXF), Polygon File Format (PLY) or any other formatsuitable for Computer-Aided Design (CAD), e.g., Wavefront (OBJ). Theconversion from DICOM data to computer object data optionally andpreferably includes one or more segmentation procedures, selected fromthe group consisting of thresholding, region growing, dynamic regiongrowing, and the like.

Thresholding procedures exploit the differences in density of differenttissues to select image pixels with a higher or equal value to aprescribed threshold value. For example, a prescribed threshold value ofa thresholding procedure can be selected so that image pixels withregard to hard tissue pass the thresholding procedure, and other imagepixels relating are filtered out. The thresholding procedure can beapplied multiple times each time using a different threshold value, soas to obtain separate datasets for different tissue types.

Region growing procedures are typically applied after thresholding toisolate areas which have the same density range. A region growingprocedure can examine neighboring pixels of initial seed points anddetermines whether the neighboring pixels belong to the region. Theprocedure is optionally and preferably performed iteratively to segmentthe image. For example seed points can be selected according todifferent tissue types and the region growing segmentation techniquescan be performed iteratively to separate image pixels as belonging toone of these tissue types. In dynamic region growing, a range of imageparameters are selected in addition to the seed points. These parametersare selected to allow recognizing an image pixel as the same as the seedpoints.

Typically, but not necessarily, an initial background segmentationprocedure is applied for removing from the DICOM data elements that donot belong to any of the tissue types of interest. Subsequentsegmentation procedures can then be applied for more refinedsegmentation of one or more refined area of a subject's anatomy by usingdifferent segmentation techniques.

Following segmentation, the conversion from DICOM data to computerobject data can also include smoothing, wrapping and/or hole-filling tocompensate for artifacts within the DICOM data. A format conversionprocedure can then be applied to the segmented DICOM data so as toprovide the computer object data in in any of the aforementionedformats.

In some embodiments of the present invention, the input data arereceived from a computer readable medium as computer object data, inwhich case it is not necessary to obtain and convert the DICOM data. Inthese embodiments, it is not necessary to execute operations 701 and702.

In any event, the computer object data preferably include datapertaining to a shape of one or more bodily structures comprising one ormore tissue elements as further detailed hereinabove. Whether obtainedby conversion of DICOM data or received directly as such, the computerobject data are optionally and preferably arranged in multiple files,each pertaining to a different bodily structure.

When the bodily structure includes shelled hollow objects havingcavities, such as, but not limited to, vessel or blood vesselstructures, the procedure optionally preferably proceeds to 752 at whichcomputer object data describing the cavities but not the shell aregenerated. The procedure can then continue to 753 at which computerobject data describing the cavities in shrunk form are generated. Thecavities described by the data at 753 are shrunk in the sense that theiroutermost surfaces encompass a volume which is reduced compared to thevolume of the cavities received as input. In other words, the cavitiesdescribed by the data at 753 have an overall outermost surface area thatis smaller than the inner surface area of the hollow object described bythe input data. A representative example of a technique suitable forbeing executed at 753 is described below. From 753 the procedureoptionally and preferably continues to 754 at which the computer objectdata describing the shelled hollow objects (e.g., the computer objectdata obtained at 702 or received from a computer readable medium) arecombined with the computer object data obtained at 753. This combinationprovides combined computer object data that describe an outermost shellencapsulating a core in a manner that there is a gap between the innersurface of the outermost shell and the outermost surface of the core. Amore detailed description of operations 752, 753 and 754 is described inExample 6, below.

Alternatively, operations 752, 753 and 754 can be skipped.

At 703 a type of the bodily structure to be mimicked by an additivemanufactured object (e.g., soft tissue, bone, muscle tissue, smoothtissue, bone tumor, cartilage, disks, nerves/spinal cord, body liquid,e.g., blood, vessel) is determined for each data file. The determinationcan be by extracting information present in the respective computerobject data file, or the respective DICOM data file, or from informationassociated with the respective data file.

At 704, a set of rules associated with the respective bodily structureis selected. The set of AM rules optionally and preferably includebuilding material formulation(s) to be dispensed as well as dispensingparameters and conditions (e.g., temperature, interlacing ratios,interlacing texture). The set of AM rules can be obtained from a look-uptable having an entry for each type of bodily structure, and a set ofadditive manufacturing parameters associated with each such entry. Theset of parameters optionally and preferably include at least one of abuilding material formulation and a combination of building materialformulations. For bodily structures that are blood vessels, andoptionally and preferably also for other type of bodily structures theset of parameters optionally and preferably also include a wallthickness of the blood vessel.

In some embodiments of the present invention a subject profile isreceived. The subject profile typically includes one or more of weight,gender, age, ethnicity, race, clinical history, etc. In some embodimentsof the present invention the subject profile also includes a geneticprofile, which can encompass the genes in an entire genome of thesubject, or it can encompass a specific subset of genes. The geneticprofile may include genomic profile, a proteomic profile, an epigenomicprofile and/or a transcriptomic profile. In embodiments in which thesubject profile is received, the look-up table also includes entries fordifferent profile parameters. Specifically, the lookup table can includeseveral entries for each type of bodily structure, one entry for eachprofile parameter. As a representative and non-limiting example, alook-up table can include several entries for, say, a blood vessel,wherein one entry for each age group.

In some embodiments of the present invention the set of AM rules areselected by the operator, for example, via a user interface (e.g., userinterface 116). Also contemplated, are embodiments in which both alook-up table and a user interface are employed. For example, thelook-up table can be used for narrowing the number of options providedto the operator, and the user interface can be used for selecting thefinal set of AM rules.

Further contemplated, are embodiments in which the set of rules arereceived together with the computer object data. For example, eachcomputer object data file can include one or more AM rules, or beassociated with AM rule file including one or more AM rules, wherein theAM rules correspond to the respective computer object data.

At 705 a slicing operation is applied, optionally and preferablyseparately for each computer object data file. The slicing is typicallyexecuted by generating, for computer object data file, a set of imagefiles, each describing a 2D voxel map of a plane characterized by adifferent vertical coordinate (e.g., the aforementioned z coordinate),which plane corresponds to a layer of the object mimicking therespective bodily structure. The image file can be in any 2D formatknown in the art, such as, but not limited to, a bitmap file (BMP),portable network graphs (PNG), or the like. A preferred slicingtechnique is provided below with reference to FIG. 28B.

At 706 two or more of the sets of image files are combined into a singleimage file. For example, image files that correspond to the samevertical coordinate but to objects mimicking different bodily structurescan be combined to provide an image file that describes a layer which,once printed, includes sliced sections of two or more objectsrespectively mimicking two or more bodily structures. At 707 the imagefile(s) is uploaded to an AM system such as, but not limited to, system10 or system 110, to fabricate non-biological objects that resembles thebodily structures.

The procedure ends at 708.

FIG. 28B is a flowchart diagram of an exemplified slicing methodaccording to some embodiments of the present invention. The method isparticularly useful for executing slicing operation 705 of FIG. 28A. Themethod begins at 720 and is optionally and preferably applied for eachvoxel in the computer object data.

At decision 721 a distance field value relative to the 3D object isdetermined for the respective voxel. The distance field value indicateswhether the voxel is within or outside the object mimicking the bodilystructure to be printed. For example, negative distance field values canbe assigned to voxels outside the object mimicking the bodily structure,positive distance field values can be assigned to voxels within theobject mimicking the bodily structure, and zero distance field valuescan be assigned to voxels on the outermost surface of the objectmimicking the bodily structure. A representative example of a techniquesuitable for determining distance field values is provided in Example 4,below.

When the voxel is within or on the outermost surface of the objectmimicking the bodily structure (for example, when the distance fieldvalue is positive), the method continues to 722 at which a buildingmaterial formulation is allocated for the respective voxel. The buildingmaterial formulation can be a modeling material formulation, a supportmaterial formulation, or a liquid material formulation, and isoptionally and preferably determined based on the position of the voxelin the 3D object and the AM rules obtained at 704 above. From 722 themethod continues to 724 at which the method selects a pixel value thatcorresponds to the allocated building material formulation. The pixelvalue can be any value that uniquely represents the allocated buildingmaterial formulation. For example, the pixel value can be a grayscalelevel or a color value (e.g., RGB value).

When the voxel is outside the object mimicking the bodily structure (forexample, when the distance field value is negative), the methodcontinues to decision 723 at which the method determine whether thevoxel is to be occupied or left vacant. If the voxel is to be leftvacant, the method continues to terminal 726, the method selects a pixelvalue that uniquely represents a vacant pixel. For example, the methodcan select a null value to represents a vacant pixel. Alternatively,when the voxel is outside the object mimicking the bodily structure themethod can continues from 723 to terminal 728 where it ends, in whichcase pixels that have not been assigned with any values are to beinterested as instructions to leave a voxel vacant.

If the voxel is to be occupied, the method continues to 725 at which abuilding material formulation is allocated to the voxel, and then to 724at which the method selects a pixel value that corresponds to theallocated building material formulation as further detailed hereinabove.

From 724, 725 or 726, as the case may be, the method continues to 727 atwhich the selected pixel value is assigned to a pixel in a 2D image,wherein the location of the pixel in the 2D image corresponds to thelocation of the voxel within the layer that is represented by the 2Dimage.

The method ends at 728.

Herein throughout, the term “bodily” when used in the context of, forexample, a structure, organ, tissue or material, describes the indicatedstructure, organ, tissue or material, as being part of a body of asubject, preferably a living subject. This term encompasses biologicalsystems, organs, tissues, cells and materials.

Herein throughout, the term “subject” encompasses animals, preferablymammals, more preferably human beings, at any age. This term encompassesindividuals who are at risk to develop the pathology or who suffer froma pathology.

The term “bodily structure” refers to a part of a body of a subject, asdescribed herein, including systems, organs, tissues, cells and asurrounding environment of any of the foregoing. A bodily structure, forexample, can comprise several organs acting together in a living body,for example, a gastrointestinal tract, a cardiovascular system, arespiratory tract, and the like. The structure can include, in additionto organs and tissues that form a part of these systems, also structuresrelated to a pathology, for example, tumor cells or tissues. A bodilystructure can alternatively include, for example, a heart and bloodvessels associated therewith. A bodily structure can alternativelyinclude an organ, such as, for example, an arm or forearm, or leg, andcan encompass the related bones system and muscle tissues, bloodvessels, tumor tissues (if present) and/or skin tissues in itssurroundings.

The term “tissue” describes a part of an organism consisting of cellsdesigned to perform a function or functions. Examples include, but arenot limited to, brain tissue, retina, skin tissue, hepatic tissue,pancreatic tissue, bone, cartilage, connective tissue, blood tissue,muscle tissue, cardiac tissue, vascular tissue, renal tissue, pulmonarytissue, gonadal tissue, hematopoietic tis sue.

According to some of any of the embodiments described herein, at leastsome, and preferably all, the building material formulations usable inthe context of the present embodiments are synthetic, non-biological,formulations, and are comprised essentially of synthetic materials.

As used herein, the term “synthetic material” describes an organicmaterial that is not inherently present in a living subject. This termencompasses non-biological organic materials, non-naturally occurringorganic materials, and/or synthetically prepared organic materials.

According to some of any of the embodiments described herein, at leastsome, and preferably all, the building material formulations usable inthe context of the present embodiments are devoid of biologicalmaterials.

By “biological material”, as used herein, it is meant organic materialsthat are inherently present in living subjects as defined herein. Suchorganic materials encompass, for example, cells and cellular components,proteins (including enzymes, hormones, receptor ligands and the like)peptides, nucleic acids, genes, amino acids.

By “devoid of” it is meant less than 1%, or less than 0.5%, or less than0.1%, or less than 0.05%, or less than 0.01%, or less than 0.005%, orless than 0.001%, and less, including null, by weight, of the totalweight of the formulation.

It is to be understood that some of the present embodiments contemplatea formulation that contains water. According to some of any of theembodiments described herein, at least some, and preferably all, thebuilding material formulations usable in the context of the presentembodiments are un-cellularized, namely, are devoid of biological cellsor cellular components.

According to some of any of the embodiments described herein, modelingmaterial formulations as described herein comprise water in an amount ofless than 10%, or less than 8%, or less than 5%, or even less, byweight, or is devoid of, as defined herein, water.

In some of any of the embodiments described herein, the curable andparticularly the non-curable materials, included in the buildingmaterial formulations and the formulation and formulation systemsdescribed herein, are non-toxic, non-environmentally hazardous, and arehence safe for use and disposal.

It is expected that during the life of a patent maturing from thisapplication many relevant material formulations will be developed andthe scope of the term material formulation is intended to include allsuch new technologies a priori, to the extent that these materialformulation exhibit the mechanical properties described herein

As used herein the term “about” refers to ±10% or ±5%.

The word “exemplary” is used herein to mean “serving as an example,instance or illustration.” Any embodiment described as “exemplary” isnot necessarily to be construed as preferred or advantageous over otherembodiments and/or to exclude the incorporation of features from otherembodiments.

The word “optionally” is used herein to mean “is provided in someembodiments and not provided in other embodiments.” Any particularembodiment of the invention may include a plurality of “optional”features unless such features conflict.

The terms “comprises”, “comprising”, “includes”, “including”, “having”and their conjugates mean “including but not limited to”.

The term “consisting of” means “including and limited to”.

The term “consisting essentially of” means that the composition, methodor structure may include additional ingredients, steps and/or parts, butonly if the additional ingredients, steps and/or parts do not materiallyalter the basic and novel characteristics of the claimed composition,method or structure.

As used herein, the singular form “a”, “an” and “the” include pluralreferences unless the context clearly dictates otherwise. For example,the term “a compound” or “at least one compound” may include a pluralityof compounds, including mixtures thereof.

Throughout this application, various embodiments of this invention maybe presented in a range format. It should be understood that thedescription in range format is merely for convenience and brevity andshould not be construed as an inflexible limitation on the scope of theinvention. Accordingly, the description of a range should be consideredto have specifically disclosed all the possible subranges as well asindividual numerical values within that range. For example, descriptionof a range such as from 1 to 6 should be considered to have specificallydisclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numberswithin that range, for example, 1, 2, 3, 4, 5, and 6. This appliesregardless of the breadth of the range.

Whenever a numerical range is indicated herein, it is meant to includeany cited numeral (fractional or integral) within the indicated range.The phrases “ranging/ranges between” a first indicate number and asecond indicate number and “ranging/ranges from” a first indicate number“to” a second indicate number are used herein interchangeably and aremeant to include the first and second indicated numbers and all thefractional and integral numerals therebetween.

As used herein the term “method” or “process” refers to manners, means,techniques and procedures for accomplishing a given task including, butnot limited to, those manners, means, techniques and procedures eitherknown to, or readily developed from known manners, means, techniques andprocedures by practitioners of the chemical, physical and engineeringarts.

Herein throughout, the term “(meth)acrylic” encompasses acrylic andmethacrylic compounds.

Herein throughout, the phrase “linking moiety” or “linking group”describes a group that connects two or more moieties or groups in acompound. A linking moiety is typically derived from a bi- ortri-functional compound, and can be regarded as a bi- or tri-radicalmoiety, which is connected to two or three other moieties, via two orthree atoms thereof, respectively.

Exemplary linking moieties include a hydrocarbon moiety or chain,optionally interrupted by one or more heteroatoms, as defined herein,and/or any of the chemical groups listed below, when defined as linkinggroups.

When a chemical group is referred to herein as “end group” it is to beinterpreted as a substituent, which is connected to another group viaone atom thereof.

Herein throughout, the term “hydrocarbon” collectively describes achemical group composed mainly of carbon and hydrogen atoms. Ahydrocarbon can be comprised of alkyl, alkene, alkyne, aryl, and/orcycloalkyl, each can be substituted or unsubstituted, and can beinterrupted by one or more heteroatoms. The number of carbon atoms canrange from 2 to 20, and is preferably lower, e.g., from 1 to 10, or from1 to 6, or from 1 to 4. A hydrocarbon can be a linking group or an endgroup.

Bisphenol A is an example of a hydrocarbon comprised of 2 aryl groupsand one alkyl group.

As used herein, the term “amine” describes both a —NR′R″ group and a—NR′— group, wherein R′ and R″ are each independently hydrogen, alkyl,cycloalkyl, aryl, as these terms are defined hereinbelow.

The amine group can therefore be a primary amine, where both R′ and R″are hydrogen, a secondary amine, where R′ is hydrogen and R″ is alkyl,cycloalkyl or aryl, or a tertiary amine, where each of R′ and R″ isindependently alkyl, cycloalkyl or aryl.

Alternatively, R′ and R″ can each independently be hydroxyalkyl,trihaloalkyl, cycloalkyl, alkenyl, alkynyl, aryl, heteroaryl,heteroalicyclic, amine, halide, sulfonate, sulfoxide, phosphonate,hydroxy, alkoxy, aryloxy, thiohydroxy, thioalkoxy, thioaryloxy, cyano,nitro, azo, sulfonamide, carbonyl, C-carboxylate, O-carboxylate,N-thiocarbamate, O-thiocarbamate, urea, thiourea, N-carbamate,O-carbamate, C-amide, N-amide, guanyl, guanidine and hydrazine.

The term “amine” is used herein to describe a —NR′R″ group in caseswhere the amine is an end group, as defined hereinunder, and is usedherein to describe a —NR′— group in cases where the amine is a linkinggroup or is or part of a linking moiety.

The term “alkyl” describes a saturated aliphatic hydrocarbon includingstraight chain and branched chain groups. Preferably, the alkyl grouphas 1 to 30, or 1 to 20 carbon atoms. Whenever a numerical range; e.g.,“1-20”, is stated herein, it implies that the group, in this case thealkyl group, may contain 1 carbon atom, 2 carbon atoms, 3 carbon atoms,etc., up to and including 20 carbon atoms. The alkyl group may besubstituted or unsubstituted. Substituted alkyl may have one or moresubstituents, whereby each substituent group can independently be, forexample, hydroxyalkyl, trihaloalkyl, cycloalkyl, alkenyl, alkynyl, aryl,heteroaryl, heteroalicyclic, amine, halide, sulfonate, sulfoxide,phosphonate, hydroxy, alkoxy, aryloxy, thiohydroxy, thioalkoxy,thioaryloxy, cyano, nitro, azo, sulfonamide, C-carboxylate,O-carboxylate, N-thiocarbamate, O-thiocarbamate, urea, thiourea,N-carbamate, O-carbamate, C-amide, N-amide, guanyl, guanidine andhydrazine.

The alkyl group can be an end group, as this phrase is definedhereinabove, wherein it is attached to a single adjacent atom, or alinking group, as this phrase is defined hereinabove, which connects twoor more moieties via at least two carbons in its chain. When the alkylis a linking group, it is also referred to herein as “alkylene” or“alkylene chain”.

Herein, a C(1-4) alkyl, substituted by a hydrophilic group, as definedherein, is included under the phrase “hydrophilic group” herein.

Alkene and Alkyne, as used herein, are an alkyl, as defined herein,which contains one or more double bond or triple bond, respectively.

The term “cycloalkyl” describes an all-carbon monocyclic ring or fusedrings (i.e., rings which share an adjacent pair of carbon atoms) groupwhere one or more of the rings does not have a completely conjugatedpi-electron system. Examples include, without limitation, cyclohexane,adamantine, norbornyl, isobornyl, and the like. The cycloalkyl group maybe substituted or unsubstituted. Substituted cycloalkyl may have one ormore substituents, whereby each substituent group can independently be,for example, hydroxyalkyl, trihaloalkyl, cycloalkyl, alkenyl, alkynyl,aryl, heteroaryl, heteroalicyclic, amine, halide, sulfonate, sulfoxide,phosphonate, hydroxy, alkoxy, aryloxy, thiohydroxy, thioalkoxy,thioaryloxy, cyano, nitro, azo, sulfonamide, C-carboxylate,O-carboxylate, N-thiocarbamate, O-thiocarbamate, urea, thiourea,N-carbamate, O-carbamate, C-amide, N-amide, guanyl, guanidine andhydrazine. The cycloalkyl group can be an end group, as this phrase isdefined hereinabove, wherein it is attached to a single adjacent atom,or a linking group, as this phrase is defined hereinabove, connectingtwo or more moieties at two or more positions thereof.

Cycloalkyls of 1-6 carbon atoms, substituted by two or more hydrophilicgroups, as defined herein, is included under the phrase “hydrophilicgroup” herein.

The term “heteroalicyclic” describes a monocyclic or fused ring grouphaving in the ring(s) one or more atoms such as nitrogen, oxygen andsulfur. The rings may also have one or more double bonds. However, therings do not have a completely conjugated pi-electron system.Representative examples are piperidine, piperazine, tetrahydrofuran,tetrahydropyrane, morpholino, oxalidine, and the like.

The heteroalicyclic may be substituted or unsubstituted. Substitutedheteroalicyclic may have one or more substituents, whereby eachsubstituent group can independently be, for example, hydroxyalkyl,trihaloalkyl, cycloalkyl, alkenyl, alkynyl, aryl, heteroaryl,heteroalicyclic, amine, halide, sulfonate, sulfoxide, phosphonate,hydroxy, alkoxy, aryloxy, thiohydroxy, thioalkoxy, thioaryloxy, cyano,nitro, azo, sulfonamide, C-carboxylate, O-carboxylate, N-thiocarbamate,O-thiocarbamate, urea, thiourea, O-carbamate, N-carbamate, C-amide,N-amide, guanyl, guanidine and hydrazine. The heteroalicyclic group canbe an end group, as this phrase is defined hereinabove, where it isattached to a single adjacent atom, or a linking group, as this phraseis defined hereinabove, connecting two or more moieties at two or morepositions thereof.

A heteroalicyclic group which includes one or more of electron-donatingatoms such as nitrogen and oxygen, and in which a numeral ratio ofcarbon atoms to heteroatoms is 5:1 or lower, is included under thephrase “hydrophilic group” herein.

The term “aryl” describes an all-carbon monocyclic or fused-ringpolycyclic (i.e., rings which share adjacent pairs of carbon atoms)groups having a completely conjugated pi-electron system. The aryl groupmay be substituted or unsubstituted. Substituted aryl may have one ormore substituents, whereby each substituent group can independently be,for example, hydroxyalkyl, trihaloalkyl, cycloalkyl, alkenyl, alkynyl,aryl, heteroaryl, heteroalicyclic, amine, halide, sulfonate, sulfoxide,phosphonate, hydroxy, alkoxy, aryloxy, thiohydroxy, thioalkoxy,thioaryloxy, cyano, nitro, azo, sulfonamide, C-carboxylate,O-carboxylate, N-thiocarbamate, urea, thiourea, N-carbamate,O-carbamate, C-amide, N-amide, guanyl, guanidine and hydrazine. The arylgroup can be an end group, as this term is defined hereinabove, whereinit is attached to a single adjacent atom, or a linking group, as thisterm is defined hereinabove, connecting two or more moieties at two ormore positions thereof.

The term “heteroaryl” describes a monocyclic or fused ring (i.e., ringswhich share an adjacent pair of atoms) group having in the ring(s) oneor more atoms, such as, for example, nitrogen, oxygen and sulfur and, inaddition, having a completely conjugated pi-electron system. Examples,without limitation, of heteroaryl groups include pyrrole, furan,thiophene, imidazole, oxazole, thiazole, pyrazole, pyridine, pyrimidine,quinoline, isoquinoline and purine. The heteroaryl group may besubstituted or unsubstituted. Substituted heteroaryl may have one ormore substituents, whereby each substituent group can independently be,for example, hydroxyalkyl, trihaloalkyl, cycloalkyl, alkenyl, alkynyl,aryl, heteroaryl, heteroalicyclic, amine, halide, sulfonate, sulfoxide,phosphonate, hydroxy, alkoxy, aryloxy, thiohydroxy, thioalkoxy,thioaryloxy, cyano, nitro, azo, sulfonamide, C-carboxylate,O-carboxylate, N-thiocarbamate, urea, thiourea, O-carbamate,N-carbamate, C-amide, N-amide, guanyl, guanidine and hydrazine. Theheteroaryl group can be an end group, as this phrase is definedhereinabove, where it is attached to a single adjacent atom, or alinking group, as this phrase is defined hereinabove, connecting two ormore moieties at two or more positions thereof. Representative examplesare pyridine, pyrrole, oxazole, indole, purine and the like.

The term “halide” and “halo” describes fluorine, chlorine, bromine oriodine.

The term “haloalkyl” describes an alkyl group as defined above, furthersubstituted by one or more halide.

The term “sulfate” describes a —O—S(═O)₂—OR′ end group, as this term isdefined hereinabove, or an —O—S(═O)₂—O— linking group, as these phrasesare defined hereinabove, where R′ is as defined hereinabove.

The term “thiosulfate” describes a —O—S(═S)(═O)—OR′ end group or a—O—S(═S)(═O)—O— linking group, as these phrases are defined hereinabove,where R′ is as defined hereinabove.

The term “sulfite” describes an —O—S(═O)—O—R′ end group or a —O—S(═O)—O—group linking group, as these phrases are defined hereinabove, where R′is as defined hereinabove.

The term “thiosulfite” describes a —O—S(═S)—O—R′ end group or an—O—S(═S)—O— group linking group, as these phrases are definedhereinabove, where R′ is as defined hereinabove.

The term “sulfinate” describes a —S(═O)—OR′ end group or an —S(═O)—O—group linking group, as these phrases are defined hereinabove, where R′is as defined hereinabove.

The term “sulfoxide” or “sulfinyl” describes a —S(═O)R′ end group or an—S(═O)— linking group, as these phrases are defined hereinabove, whereR′ is as defined hereinabove.

The term “sulfonate” describes a —S(═O)₂—R′ end group or an —S(═O)₂—linking group, as these phrases are defined hereinabove, where R′ is asdefined herein.

The term “S-sulfonamide” describes a —S(═O)₂—NR′R″ end group or a—S(═O)₂—NR′— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

The term “N-sulfonamide” describes an R'S(═O)₂—NR″— end group or a—S(═O)₂—NR′— linking group, as these phrases are defined hereinabove,where R′ and R″ are as defined herein.

The term “disulfide” refers to a —S—SR′ end group or a —S—S— linkinggroup, as these phrases are defined hereinabove, where R′ is as definedherein.

The term “phosphonate” describes a —P(═O)(OR′)(OR″) end group or a—P(═O)(OR′)(O)— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

The term “thiophosphonate” describes a —P(═S)(OR′)(OR″) end group or a—P(═S)(OR′)(O)— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

The term “phosphinyl” describes a —PR′R″ end group or a —PR′— linkinggroup, as these phrases are defined hereinabove, with R′ and R″ asdefined hereinabove.

The term “phosphine oxide” describes a —P(═O)(R′)(R″) end group or a—P(═O)(R′)— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

The term “phosphine sulfide” describes a —P(═S)(R′)(R″) end group or a—P(═S)(R′)— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

The term “phosphite” describes an —O—PR′(═O)(OR″) end group or an—O—PH(═O)(O)— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

The term “carbonyl” or “carbonate” as used herein, describes a —C(═O)—R′end group or a —C(═O)— linking group, as these phrases are definedhereinabove, with R′ as defined herein.

The term “thiocarbonyl” as used herein, describes a —C(═S)—R′ end groupor a —C(═S)— linking group, as these phrases are defined hereinabove,with R′ as defined herein.

The term “oxo” as used herein, describes a (═O) group, wherein an oxygenatom is linked by a double bond to the atom (e.g., carbon atom) at theindicated position.

The term “thiooxo” as used herein, describes a (═S) group, wherein asulfur atom is linked by a double bond to the atom (e.g., carbon atom)at the indicated position.

The term “oxime” describes a=N—OH end group or a=N—O— linking group, asthese phrases are defined hereinabove.

The term “hydroxyl” describes a —OH group.

The term “alkoxy” describes both an —O-alkyl and an —O-cycloalkyl group,as defined herein.

The term “aryloxy” describes both an —O-aryl and an —O-heteroaryl group,as defined herein.

The term “thiohydroxy” describes a —SH group.

The term “thioalkoxy” describes both a —S-alkyl group, and a—S-cycloalkyl group, as defined herein.

The term “thioaryloxy” describes both a —S-aryl and a —S-heteroarylgroup, as defined herein.

The “hydroxyalkyl” is also referred to herein as “alcohol”, anddescribes an alkyl, as defined herein, substituted by a hydroxy group.

The term “cyano” describes a —C≡N group.

The term “isocyanate” describes an —N═C═O group.

The term “isothiocyanate” describes an —N═C═S group.

The term “nitro” describes an —NO₂ group.

The term “acyl halide” describes a —(C═O)R″″ group wherein R″″ ishalide, as defined hereinabove.

The term “azo” or “diazo” describes an —N═NR′ end group or an —N═N—linking group, as these phrases are defined hereinabove, with R′ asdefined hereinabove.

The term “peroxo” describes an —O—OR′ end group or an —O—O— linkinggroup, as these phrases are defined hereinabove, with R′ as definedhereinabove.

The term “carboxylate” as used herein encompasses C-carboxylate andO-carboxylate.

The term “C-carboxylate” describes a —C(═O)—OR′ end group or a —C(═O)—O—linking group, as these phrases are defined hereinabove, where R′ is asdefined herein.

The term “O-carboxylate” describes a —OC(═O)R′ end group or a —OC(═O)—linking group, as these phrases are defined hereinabove, where R′ is asdefined herein.

A carboxylate can be linear or cyclic. When cyclic, R′ and the carbonatom are linked together to form a ring, in C-carboxylate, and thisgroup is also referred to as lactone.

Alternatively, R′ and O are linked together to form a ring inO-carboxylate. Cyclic carboxylates can function as a linking group, forexample, when an atom in the formed ring is linked to another group.

The term “thiocarboxylate” as used herein encompasses C-thiocarboxylateand O-thiocarboxylate.

The term “C-thiocarboxylate” describes a —C(═S)—OR′ end group or a—C(═S)—O— linking group, as these phrases are defined hereinabove, whereR′ is as defined herein.

The term “O-thiocarboxylate” describes a —OC(═S)R′ end group or a—OC(═S)— linking group, as these phrases are defined hereinabove, whereR′ is as defined herein.

A thiocarboxylate can be linear or cyclic. When cyclic, R′ and thecarbon atom are linked together to form a ring, in C-thiocarboxylate,and this group is also referred to as thiolactone. Alternatively, R′ andO are linked together to form a ring in O-thiocarboxylate. Cyclicthiocarboxylates can function as a linking group, for example, when anatom in the formed ring is linked to another group.

The term “carbamate” as used herein encompasses N-carbamate andO-carbamate.

The term “N-carbamate” describes an R″OC(═O)—NR′— end group or a—OC(═O)—NR′— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

The term “O-carbamate” describes an —OC(═O)—NR′R″ end group or an—OC(═O)—NR′— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

A carbamate can be linear or cyclic. When cyclic, R′ and the carbon atomare linked together to form a ring, in O-carbamate. Alternatively, R′and O are linked together to form a ring in N-carbamate. Cycliccarbamates can function as a linking group, for example, when an atom inthe formed ring is linked to another group.

The term “carbamate” as used herein encompasses N-carbamate andO-carbamate.

The term “thiocarbamate” as used herein encompasses N-thiocarbamate andO-thiocarbamate.

The term “O-thiocarbamate” describes a —OC(═S)—NR′R″ end group or a—OC(═S)—NR′— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

The term “N-thiocarbamate” describes an R″OC(═S)NR′— end group or a—OC(═S)NR′— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

Thiocarbamates can be linear or cyclic, as described herein forcarbamates.

The term “dithiocarbamate” as used herein encompasses S-dithiocarbamateand N-dithiocarbamate.

The term “S-dithiocarbamate” describes a —SC(═S)—NR′R″ end group or a—SC(═S)NR′— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

The term “N-dithiocarbamate” describes an R″SC(═S)NR′— end group or a—SC(═S)NR′— linking group, as these phrases are defined hereinabove,with R′ and R″ as defined herein.

The term “urea”, which is also referred to herein as “ureido”, describesa —NR′C(═O)—NR″R′″ end group or a —NR′C(═O)—NR″— linking group, as thesephrases are defined hereinabove, where R′ and R″ are as defined hereinand R′″ is as defined herein for R′ and R″.

The term “thiourea”, which is also referred to herein as “thioureido”,describes a —NR′—C(═S)—NR″R′″ end group or a —NR′—C(═S)—NR″— linkinggroup, with R′, R″ and R′″ as defined herein.

The term “amide” as used herein encompasses C-amide and N-amide.

The term “C-amide” describes a —C(═O)—NR′R″ end group or a —C(═O)—NR′—linking group, as these phrases are defined hereinabove, where R′ and R″are as defined herein.

The term “N-amide” describes a R′C(═O)—NR″— end group or a R′C(═O)—N—linking group, as these phrases are defined hereinabove, where R′ and R″are as defined herein.

An amide can be linear or cyclic. When cyclic, R′ and the carbon atomare linked together to form a ring, in C-amide, and this group is alsoreferred to as lactam. Cyclic amides can function as a linking group,for example, when an atom in the formed ring is linked to another group.

The term “guanyl” describes a R′R″NC(═N)— end group or a —R′NC(═N)—linking group, as these phrases are defined hereinabove, where R′ and R″are as defined herein.

The term “guanidine” describes a —R′NC(═N)—NR″R′″ end group or a—R′NC(═N)—NR″— linking group, as these phrases are defined hereinabove,where R′, R″ and R′″ are as defined herein.

The term “hydrazine” describes a —NR′—NR″R′″ end group or a —NR′—NR″—linking group, as these phrases are defined hereinabove, with R′, R″,and R′″ as defined herein.

As used herein, the term “hydrazide” describes a —C(═O)—NR′—NR″R′″ endgroup or a —C(═O)—NR′—NR″— linking group, as these phrases are definedhereinabove, where R′, R″ and R′″ are as defined herein.

As used herein, the term “thiohydrazide” describes a —C(═S)—NR′—NR″R′″end group or a —C(═S)—NR′—NR″— linking group, as these phrases aredefined hereinabove, where R′, R″ and R′″ are as defined herein.

As used herein, the term “alkylene glycol” describes a—O—[(CR′R″)_(z)—O]_(y)—R′″ end group or a —O—[(CR′R″)_(z)—O]_(y)—linking group, with R′, R″ and R′″ being as defined herein, and with zbeing an integer of from 1 to 10, preferably, from 2 to 6, morepreferably 2 or 3, and y being an integer of 1 or more. Preferably R′and R″ are both hydrogen. When z is 2 and y is 1, this group is ethyleneglycol. When z is 3 and y is 1, this group is propylene glycol. When yis 2-4, the alkylene glycol is referred to herein as oligo(alkyleneglycol).

When y is greater than 4, the alkylene glycol is referred to herein aspoly(alkylene glycol). In some embodiments of the present invention, apoly(alkylene glycol) group or moiety can have from 10 to 200 repeatingalkylene glycol units, such that z is 10 to 200, preferably 10-100, morepreferably 10-50.

The term “silanol” describes a —Si(OH)R′R″ group, or —Si(OH)₂R′ group or—Si(OH)₃ group, with R′ and R″ as described herein.

The term “silyl” describes a —SiR′R″R′″ group, with R′, R″ and R′″ asdescribed herein.

As used herein, the term “urethane” or “urethane moiety” or “urethanegroup” describes a Rx-O—C(═O)—NR′R″ end group or a —Rx-O—C(═O)—NR′—linking group, with R′ and R″ being as defined herein, and Rx being analkyl, cycloalkyl, aryl, alkylene glycol or any combination thereof.Preferably R′ and R″ are both hydrogen.

The term “polyurethane” or “oligourethane” describes a moiety thatcomprises at least one urethane group as described herein in therepeating backbone units thereof, or at least one urethane bond,—O—C(═O)—NR′—, in the repeating backbone units thereof.

It is appreciated that certain features of the invention, which are, forclarity, described in the context of separate embodiments, may also beprovided in combination in a single embodiment. Conversely, variousfeatures of the invention, which are, for brevity, described in thecontext of a single embodiment, may also be provided separately or inany suitable subcombination or as suitable in any other describedembodiment of the invention. Certain features described in the contextof various embodiments are not to be considered essential features ofthose embodiments, unless the embodiment is inoperative without thoseelements.

Various embodiments and aspects of the present invention as delineatedhereinabove and as claimed in the claims section below find experimentalsupport in the following examples.

EXAMPLES

Reference is now made to the following examples, which together with theabove descriptions illustrate some embodiments of the invention in a nonlimiting fashion.

Example 1 Soft Material Formulation

The building material formulations usable in the additive manufacturingprocess described herein in any of the respective embodiments comprises,in some embodiments, at least one modeling material formulation whichfeatures (exhibits, characterized by), when hardened, a Shore A hardnesslower than 10 or a Shore 00 hardness lower than 40. Such a formulationis also referred to herein as “soft material formulation” or “softmaterial modeling formulation” or “soft modeling formulation”.

Herein and in the art, the term “hardness” describes a resistance of amaterial to permanent indentation, when measured under the specifiedconditions. Shore A hardness, which also referred to as Hardness ShA oras Shore scale A hardness, for example, is determined following the ASTMD2240 standard using a digital Shore A hardness durometer. Shore 00hardness, which also referred to as Hardness Sh00 or as Shore scale 00hardness, for example, is determined following the ASTM D2240 standardusing a digital Shore 00 hardness durometer. D, A and 00 are commonscales of hardness values, and each is measured using a respectivedurometer.

In some of any of the embodiments described herein, a soft materialformulation as described herein features, when hardened, Shore Ahardness in a range of from 0 to about 10, including any intermediatevalues and subranges therebetween.

In some of any of the embodiments described herein, a soft materialformulation as described herein features, when hardened, Shore 00hardness in a range of from 0 to about 40, or from 0 to about 30, orfrom 0 to about 20, or, for example, of from about 10 to about 20, orfrom about 10 to about 30, including any intermediate values andsubranges therebetween.

Another parameter demonstrating the low hardness of a soft materialobtainable for a hardened soft material formulation as described hereinis the compression modulus.

By “Compression Modulus” it is meant herein the ratio of mechanicalstress to strain in a material when that material is being compressed.Compression modulus can also be regarded as a modulus of elasticityapplied to a material under compression. In some embodiments,compression modulus is determined according to ASTM D695. In someembodiments, compression modulus is determined for a cylindricaluncoated object (printed of a tested soft formulation per se) featuringa radius of 20 mm and a height of 15 mm, printed using Stratasys J750™3D Printer. The test is performed using a Lloyd instrumental system,100N load cell, operated at the following parameters:Direction=Compression; Preload/Stress=0.5 N; preload/Stress Speed=50mm/minute; Speed=50 mm/minute; Limit=8 mm. A stress vs. strain data isextracted from the obtained data and the slope between strain values of0.001-0.01 was calculated. The data obtained in these tests can beexpressed as compression stress at 40% strain, or as the slope of astress vs. strain curve, when measured in a compression mode, taken atstrain values of from 0.001 to 0.01.

Same Lloyd system can be used in adhesion tests, operated at thefollowing parameters: Direction=Tension; Speed down=2 mm/minute; Speedup=5 mm/minute; Force down=−5N; Holding time=1 second. Specimens inwhich a tested soft formulation is used as a coat are measured, andresults are reported as the maximum load required to pull out the platenfrom the coat specimen.

Compression modulus can alternatively be determined, for example, for acylindrical, Agilus30-coated object made of the tested soft formulation,featuring a radius of 20 mm and a height of 15 mm, printed usingStratasys J750™ 3D Printer. The test is performed using a Lloydinstrumental system, 100N load cell, operated at the followingparameters: Direction=Compression; Preload/Stress=0.5 N; preload/StressSpeed=50 mm/minute; Speed=50 mm/minute; Limit=90N. The compressionmodulus is determined for a maximum stress value of 90N. A stress vs.strain data can be extracted from the obtained data and the slopebetween strain values of 0.001-0.01 was calculated.

In some of any of the embodiments described herein, a soft materialformulation as described herein features, when hardened. CompressionModulus of at least 0.01 MPa.

In some embodiments, a soft material formulation as described hereinfeatures, when hardened, Compression Modulus (as defined herein) of fromabout 0.01 to about 0.2 MPa, or from about 0.02 to about 0.2 MPa, fromabout 0.1 to about 0.1 MPa, or from about 0.02 to about 0.1 MPa, or fromabout 0.03 to about 0.07 MPa, including any intermediate value andsubranges therebetween.

In some embodiments, a soft material formulation as described hereinfeatures, when hardened, in addition to its low hardness, at least amoderate Tear resistance.

Tear Resistance (TR) describes the force required to tear a material,whereby the force acts substantially parallel to the major axis of thesample. Tear Resistance, when measured according to ASTM D 624 can beused to measure the resistance to the formation of a tear (tearinitiation) and the resistance to the expansion of a tear (tearpropagation). Typically, a sample is held between two holders and auniform pulling force is applied until deformation occurs. TearResistance is then calculated by dividing the force applied by thethickness of the material. Materials with low Tear Resistance tend tohave poor resistance to abrasion.

In some embodiments, the Tear resistance is determined in accordancewith ASTM D624 for a specimen as described therein having a thickness of2 mm. Values are reported as Load at maximum Load (N) for a 2 mm-thickspecimen. Time to Break can also be measured in this test. The reportedvalues can be converted to N/m Tear Resistance values when divided by0.002. For example, a value of 0.3N equals 150 N/m.

Load to break can be determined for a cubic Agilus-coated object made ofthe tested formulation, having dimensions of 50×50×50 mm, printed usingStratasys J750™ 3D Printer. The test is performed using a Lloydinstrumental system, 100N load cell, operated at the followingparameters: Direction=Compression; Preload/Stress=0.5 N; preload/StressSpeed=50 mm/minute; Speed=50 mm/minute; load to break is determined asthe maximum load the sample can hold before ultimate failure.

In some of any of the embodiments described herein, a soft materialformulation described herein features, when hardened, Tear resistance ofat least 100 N/m, as determined by ASTM D 624 for a specimen having athickness of 2 mm.

In some embodiments, a soft material formulation described hereinfeatures, when hardened, Tear resistance, as determined by ASTM D 624for a specimen having a thickness of 2 mm, of at least 150 N, and insome embodiments, it features Tear resistance of from 150 N/m to 500 Nm,or from 150 to 400 N/m, or from 200 N/m to 400 N/m, or from 200 N/m to350 N/m, including any intermediate values and subranges therebetween.

In some embodiments, Tear Resistance measurements are used to determinealso the time to break of a specimen under the applied pulling force.

In some embodiments, a soft material formulation as described hereinfeatures, when hardened, a time to break, as measured by ASTM D 624 fora specimen having a thickness of 2 mm, of at least 9 seconds, forexample, from 9 to 50, or from 9 to 40 or from 9 to 30, or from 15 to 30seconds.

In some of any of the embodiments described herein, a soft modelingformulation as described herein is characterized by good reactivity,that is, the dispensed layers comprising the formulation are hardenedwhen exposed to a curing condition within a time period of less than 1second, and/or a hardened layer made of the soft modeling formulationexhibits good adhesion (e.g., as demonstrated in the following).

In some embodiments, a soft modeling formulation as described herein ischaracterized by a liquid to solid transition within 1 second uponexposure to a curing condition. In some of these embodiments, the curingcondition is UV irradiation, for example, UV irradiation at 1 W/cm². Insome embodiments, the UV irradiation is by a UV Mercury (Hg) arc lamp(Medium pressure, metal-halide). In some embodiments, a soft modelingformulation as described herein is characterized by a liquid to solidtransition within 1 second upon exposure to a curing condition (e.g., UVirradiation at wavelength of from about 300 nm to about 450 nm and powerdensity of about 1 W/cm², for example using a 250 W mercury arc lamp).

The time period required for liquid to solid transition can bedetermined using DSC measurements, as known in the art.

In some of any of the embodiments described herein, a soft modelingmaterial formulation as described herein is characterized by goodcompatibility with the AM system, that is, it meets the system operationrequirements (e.g., in terms of viscosity and viscosity stability,thermal stability, etc., as described hereinabove).

In some of any of the embodiments described herein, a soft modelingmaterial formulation as described herein is characterized by goodcompatibility with an AM which is 3D inkjet printing, that is, it isjettbale, compatible with inkjet printing heads, and features aviscosity suitable for use with inkjet printing heads as describedherein and a viscosity stability at 25-75° C., for at least 24,preferably at least 48, hours.

In some of any of the embodiments described herein, a soft modelingformulation as described herein is characterized by stability(shelf-life stability) of at least one month, or at least 2, 3, 4, 5 andeven at least 6 months, that is, the formulations features substantiallythe same properties (e.g., any of the properties described herein) uponstorage for the indicated time period.

In some of any of the embodiments described herein, a soft modelingformulation as described herein is characterized by stability(shelf-life stability) of at least one month, or at least 2, 3, 4, 5 andeven at least 6 months, that is, the formulations features substantiallythe same appearance (e.g., color) upon storage (e.g., at roomtemperature) for the indicated time period.

Stability can be determined for uncoated objects (printed of a testedsoft formulation per se) or for coated objects (printed with a 0.8 mmcoating of an elastomeric curable material (for example, the Agilusfamily, e.g., Agilus30™), all printed using Stratasys J750™ 3D Printer,and featuring a cube shape of 25 mm×25 mm×25 mm, weighing the obtainedobject once printed, storing the object at 50° C. for 7 days, andre-weighing, using analytical scales, to provide the weight change in %wt., relative to the initial weight after printing.

Stability can also be measured for an Agilus-coated cubic object,printed of a tested formulation per se, using Stratasys J750™ 3DPrinter, featuring 50 mm×50 mm×50 mm dimensions; weighing the obtainedobject once printed, storing the object at 50° C. for 3 days, andre-weighing, using analytical scales. The weight change is provided in %wt., relative to the initial weight after printing.

Stability was also measured in terms of color change over time, byobserving color change after a period of 4 weeks at room temperature.

Dimensional stability can be determined, for example, for coated ovalobjects of 60×24×18 mm coated with 0.6 mm layer of an elastomericcurable material (for example, the Agilus family, e.g., Agilus30™), uponstorage at 50° C. for several days or at room temperature for one month,and observing distortions in the object upon storage.

Stickiness after printing can be determined, for example, qualitatively,for a printed object shaped as a cube, by applying to the object atissue paper and provide a rate on a 0-3 scale as follows: 3 for caseswhere the tissue paper could not be removed from the object, and 0 forcases where no fibers were stuck to the object once the tissue paper hasbeen removed.

According to some of any of the embodiments described herein, the softmaterial formulation is a curable formulation and in some embodimentsthe formulation is curable by comprising materials that arepolymerizable when exposed to a curing condition (e.g., curing energy),as described herein. It is noted that, as described in further detailhereinbelow, not all the materials in the curable formulation should becurable to render a formulation curable. Thus, herein throughout, andwith respect to any formulation described herein, a formulation isdefined as curable when at least one of the materials in the formulationis curable, or polymerizable, when exposed to a curing condition.

According to some of any of the embodiments described herein, theformulation is a synthetic, non-biological, formulation, and iscomprised essentially of synthetic materials, as defined herein.

According to some of any of the embodiments described herein, theformulation comprises water in an amount of less than 10%, or less than8%, or less than 5%, or even less, by weight, or is devoid of, asdefined herein, water.

According to some of any of the embodiments described herein, theformulation is such that does not form a hydrogel when exposed to acuring condition.

As used herein and in the art, the term “hydrogel” describes a materialcomprising a three-dimensional fibrous network as a solid phase, and anaqueous solution encaged within the fibrous network. A hydrogeltypically includes at least 80%, typically at least 85%, by weight,water.

Any formulation that features Shore hardness as indicated, preferably incombination with one or more, preferably all, of the other featuresdescribed herein is contemplated in the additive manufacturing processdescribed herein.

According to some embodiments of any of the embodiments describedherein, a soft modeling material formulation comprises a combination ofcurable materials and non-curable polymeric material.

Herein, the phrase “non-curable” with respect to a material in the softformulation means that the material does not solidify when exposed to acuring condition at which the curable materials solidify. A non-curablematerial can be a material that is devoid of polymerizable and/orcross-linkable groups, or can include polymerizable and/orcross-linkable groups yet polymerization and/or cross-linking is noteffected when exposed to a curing condition at which the curablematerials solidify.

In some embodiments, the non-curable material is devoid of polymerizableand/or cross-linkable groups.

Exemplary soft material formulations suitable for use in the context ofthe present embodiments, and which meet the process requirements, theobject requirements (e.g., as featuring a hardness of a soft bodilytissue as described herein), and are compatible with an elastomericcurable formulation, are presented hereinafter.

Such soft modeling formulations are obtained by manipulating the typeand amount of the non-curable material(s) and the type and amount ofcurable materials, such that properties such as printability,compatibility with other curable formulations, and mechanicalperformance of the printed object are provided.

According to some of any of the embodiments described herein, the softmodeling material formulation comprises curable materials andnon-curable materials, and a total amount of the non-curable materialsranges from about 10 to about 49, or from about 10 to about 30, % byweight, of the total weight of the soft modeling formulation, includingany intermediate values and subranges therebetween.

In some embodiments, a total amount of the non-curable polymericmaterials ranges from 20 to 40, or from 25 to 40, % by weight, of thetotal weight of the soft modeling formulation, including anyintermediate values and subranges therebetween.

According to some of any of the embodiments described herein, the softmodeling material formulation comprises curable materials andnon-curable materials, and a ratio of the total amount of the curablematerials and the amount of the non-curable polymeric material rangesfrom 4:1 to 1.1:1, or from 3:1 to 2:1, including any intermediate valuesand subranges therebetween.

According to some of any of the embodiments described herein, a totalamount of the curable materials ranges from about 55 to about 70 weightpercents, of the total weight of the soft modeling formulation,including any intermediate values and subranges therebetween.

According to some of any of the embodiments described herein, thecurable materials comprise at least one mono-functional curable materialand at least one multi-functional curable material.

According to some of any of the embodiments described herein, an amountof the mono-functional curable material ranges from about 50% to about89% by weight of the total weight of the soft material formulation,including any intermediate values and subranges therebetween.

According to some of any of the embodiments described herein, an amountof the multi-functional curable material ranges from about 1% to about10% by weight of the total weight of the soft material formulation,including any intermediate values and subranges therebetween.

According to some of any of the embodiments described herein, a softmodeling material formulation as described herein comprises amono-functional curable material, a multi-functional curable materialand a non-curable polymeric material.

In some of any of the embodiments described herein, the formulationcomprises more than 50%, by weight, of curable materials, that is, atotal amount of the mono-functional and multi-functional curablematerials is at least 51%, by weight, of the total weight of theformulation.

In some of any of the embodiments described herein, a total amount ofthe mono-functional and multi-functional curable materials ranges from51% to 90% or to 89%, by weight, and in some embodiments, it ranges from55% to 70%, by weight, of the total weight of the formulation, includingany intermediate values and subranges therebetween.

In some of any of the embodiments described herein, a total amount ofthe mono-functional curable material(s) ranges from 50% to 60%, or from55% to 60%, by weight, of the total weight of the formulation, includingany intermediate value and subranges therebetween.

In some of any of the embodiments described herein, a total amount ofthe multi-functional curable material(s) ranges from 3% to 10%, or from5% to 10%, or is, for example, 7%, by weight, of the total weight of theformulation, including any intermediate value and subrangestherebetween.

In some of any of the embodiments described herein, a total amount ofthe non-curable material ranges from 10% to 49%, or from 20% to 45%, orfrom 25% to 40%, by weight, of the total weight of the formulation,including any intermediate value and subranges therebetween.

In some of any of the embodiments described herein, the formulationcomprises:

-   -   a mono-functional curable material, as described herein in any        of the respective embodiments, in an amount of from 50 to 89        weight percents of the total weight of the formulation,        including any intermediate value and subranges therebetween;    -   a non-curable polymeric material, as described herein in any of        the respective embodiments, in an amount ranging from 10 to 49        weight percents of the total weight of the formulation,        including any intermediate value and subranges therebetween; and    -   a multi-functional curable material, as described herein in any        of the respective embodiments, in an amount ranging from 1 to 10        weight percents of the total weight of the formulation,        including any intermediate value and subranges therebetween.

In some of any of the embodiments described herein, a ratio of the totalamount of said mono-functional and said multi-functional curablematerials and the amount of said non-curable polymeric material rangesfrom 4:1 to 1.1:1, or from 3:1 to 2:1, including any intermediate valuesand subranges therebetween.

In some of any of the embodiments described herein, the curable and/ornon-curable materials comprised in the formulation are selected suchthat:

-   -   (i) the non-curable polymeric material features a molecular        weight of at least 1000, or at least 1500 or at least 2000        Daltons; and/or    -   (ii) the non-curable polymeric material features a Tg lower than        0, or lower than −10, or lower than −20, ° C.; and/or    -   (iii) at least 80 weight percents of the total amount of the        mono-functional and the multi-functional curable materials        include curable materials featuring, when hardened, a Tg lower        than 0, or lower than −10, or lower than −20, ° C.

In some of any of the embodiments described herein, the curable and/ornon-curable materials comprised in the formulation are selected suchthat:

-   -   the non-curable polymeric material features a molecular weight        of at least 1000, or at least 1500 or at least 2000 Daltons; and        the non-curable polymeric material features a Tg lower than 0,        or lower than −10, or lower than −20, ° C.; and/or    -   at least 80 weight percents of the total amount of the        mono-functional and the multi-functional curable materials        include curable materials featuring, when hardened, a Tg lower        than 0, or lower than −10, or lower than −20, ° C.

In some of any of the embodiments described herein, the curable and/ornon-curable materials comprised in the formulation are selected suchthat at least 80 weight percents of the total amount of themono-functional and the multi-functional curable materials includecurable materials featuring, when hardened, a Tg lower than 0, or lowerthan −10, or lower than −20, ° C. In some such embodiments, at least85%, or at least 90%, or at least 95%, or 100%, by weight, of the totalweight of the mono-functional and multi-functional curable materialsinclude curable materials featuring, when hardened, a Tg lower than 0,or lower than −10, or lower than −20, ° C.

In some of any of the embodiments described herein, the curable and/ornon-curable materials comprised in the formulation are selected suchthat at least 80 weight percents of the total amount of themono-functional and the multi-functional curable materials, as describedherein, include curable materials featuring, when hardened, a Tg lowerthan −20° C.

In some of any of the embodiments described herein, the curable and/ornon-curable materials comprised in the formulation are selected suchthat:

-   -   the non-curable polymeric material features a molecular weight        of at least 1000, or at least 1500 or at least 2000 Daltons, as        described herein; and the non-curable polymeric material        features a Tg lower than 0, or lower than −10, or lower than        −20, ° C., as described herein; and at least 80 weight percents        of the total amount of the mono-functional and the        multi-functional curable materials, as described herein, include        curable materials featuring, when hardened, a Tg lower than −20°        C.

In some of any of the embodiments described herein, the curable and/ornon-curable materials comprised in the formulation are selected suchthat:

-   -   the non-curable polymeric material features a molecular weight        of at least 2000 Daltons, as described herein; the non-curable        polymeric material features a Tg lower than −20° C., as        described herein; and at least 80 weight percents of the total        amount of the mono-functional and the multi-functional curable        materials, as described herein, include curable materials        featuring, when hardened, a Tg lower than 0, or lower than −10,        or lower than −20, ° C., as described herein.

Herein throughout, “Tg” refers to glass transition temperature definedas the location of the local maximum of the E″ curve, where E″ is theloss modulus of the material as a function of the temperature.

Broadly speaking, as the temperature is raised within a range oftemperatures containing the Tg temperature, the state of a material,particularly a polymeric material, gradually changes from a glassy stateinto a rubbery state.

Herein, “Tg range” is a temperature range at which the E″ value is atleast half its value (e.g., can be up to its value) at the Tgtemperature as defined above.

Without wishing to be bound to any particular theory, it is assumed thatthe state of a polymeric material gradually changes from the glassystate into the rubbery state within the Tg range as defined above.Herein, the term “Tg” refers to any temperature within the Tg range asdefined herein.

Herein, the phrase “molecular weight”, abbreviated as MW, when referringto a polymeric material, refers to the value known in the art as Mw,describing Weight Average Molecular Weight of the polymeric material.

Herein throughout, whenever the phrase “weight percents”, or “% byweight” or “% wt.”, is indicated in the context of embodiments of amodeling formulation, it is meant weight percents of the total weight ofthe respective uncured modeling formulation.

The Non-Curable Polymeric Material:

In some of any of the embodiments described herein, the non-curablematerial features a molecular weight of at least 500, or at least 1000,or at least 1500 or at least 2000 Daltons, for example, a molecularweight that ranges from 500 to 4000, or from 900 to 4000, preferablyfrom 1000 to 4000, or from 1500 to 4000 or, more preferably from 2000 to4000, or from 2500 to 4000, or from 1500 to 3500, Daltons, including anyintermediate value and subranges therebetween.

In some of any of the embodiments described herein, the non-curablematerial features a Tg lower than 0, or lower than −10, or lower than−20, ° C., for example, a Tg in the range of from 0 to −40° C., or from−20 to −40° C., including any intermediate value and subrangestherebetween.

In some of any of the embodiments described herein, the non-curablematerial features a molecular weight of at least 1000, or at least 1500or at least 2000 Daltons, as described herein; and a Tg lower than 0, orlower than −10, or lower than −20, ° C., as described herein.

In some embodiments, the non-curable material features essentially thesame properties (e.g., molecular weight and/or Tg) in the modelingmaterial formulation and in the hardened (soft) material obtained uponcuring.

As used herein, the term “polymeric” with reference to a materialencompasses polymers and co-polymers, including block co-polymers.

Herein, the term “block co-polymer” describes a copolymer consisting ofregularly or statistically alternating two or more different homopolymerblocks that differ in composition or structure. Each homopolymer blockin a block copolymer represents polymerized monomers of one type.

Polymeric materials featuring the above-mentioned MW and/or Tg, include,for example, polymers or block co-polymers that comprise one or morepoly(alkylene glycol)s, as defined herein, including, for example, poly(ethylene glycol), poly(propylene glycol) and block co-polymers thereof(e.g., Pluronic® block copolymers).

In some of any of the embodiments described herein, the non-curablepolymeric material comprises polypropylene glycol.

In some embodiments, the non-curable polymeric material ispoly(propylene glycol), and in some embodiments it is a polypropyleneglycol having a MW of about 2000 Daltons, or higher (e.g., 2000, 2200,2400, 2500, 2600, 2800, or 3000, Daltons, or any intermediate valuebetween these values, or of higher MW).

In some embodiments, the non-curable polymeric material is a blockco-polymer that comprises at least one polypropylene glycol block.

In some embodiments, the non-curable polymeric material is a blockco-polymer that comprises one or more polypropylene glycol block(s) andone or more polyethylene glycol block(s). Such block copolymer can be,for example, comprised of PEG-PPG-PEG, or of PEG-PPG, or ofPEG-PPG-PEG-PPG, or of PPG-PEG-PPG, or of any other number of blocks, inany combination and in any order.

In some of these embodiments, a total amount of poly(ethylene glycol) inthe block co-polymer is no more than 10 weight percents.

Thus, for example, in the exemplary block copolymers listed hereinabove,the length of the PEG blocks is such that the total amount of PEG is nomore than 10% by weight. As representative, non-limiting example, aPEG-PPG-PEG block copolymer according to these embodiments comprises PEG(A % wt.)-PPG (B % wt.)-PEG (C % wt.), wherein A+C≤10 and B≥90,respectively, for example, A+C=10 and B=90, or wherein A+C=7 and B=93,or wherein A+C=5 and B=95. Similarly, a PPG-PEG-PPG block copolymercomprises PPG (A % wt.)-PEG (B % wt.)-PPG (C % wt.), wherein A+C≥90 andB≤10, respectively, for example, A+C=90 and B=10, or wherein A+C=93 andB=7, or wherein A+C=95 and B=5.

In some of any of the embodiments described herein, the block co-polymerhas a MW of at least 2000 Daltons.

In some of any of the embodiments described herein for a PEG and PPGblock copolymer, a ratio of the number of polypropylene glycol blocksand the number of polyethylene glycol blocks is at least 1.2:1, or atleast 1.5:1 or at least 2:1. An exemplary such block copolymer isPPG-PEG-PPG. Another exemplary block copolymer is PPG-PEG-PPG-PEG-PPG.

Alternatively, or in addition, in some of any of the embodimentsdescribed herein for a PEG and PPG block copolymer, a ratio of the totalnumber of polypropylene glycol backbone units and the total number ofpolyethylene glycol backbone units in the block copolymer is at least2:1, or at least 3:1 or at least 4:1, or at least 5:1, or at least 6:1.An exemplary such block copolymer is PEG-PPG-PEG co-polymer, orPEG-PPG-PEG-PPG, or PEG-PPG-PEG-PPG-PEG, featuring such a ratio.

In some of any of the embodiments described herein, the non-curablematerial is characterized by low solubility (e.g., lower than 20% orlower than 10%, or lower), or insolubility, in water.

In the context of these embodiments, the phrase “water solubility”describes the weight % of a polymeric material that is added to 100grams water before the solution becomes turbid (non-transparent).

In some of any of the embodiments described herein, the non-curablematerial is characterized by low miscibility (e.g., lower than 20% orlower than 10%, or lower), or is immiscible, in water.

The Mono-Functional Polymeric Material:

In some of any of the embodiments described herein, the mono-functionalcurable material features, when hardened, a Tg lower than −10, or lowerthan −20° C., for example, a Tg in the range of from 0 to −40° C., orfrom −20 to −40° C., including any intermediate value and subrangestherebetween.

In some of any of the embodiments described herein, mono-functionalcurable materials usable in the context of the present embodiments canbe represented by the Formula:

P—R

wherein P is a polymerizable group and R is a hydrocarbon, as describedherein, optionally substituted by one or more substituents as describedherein, and further optionally interrupted by one or more heteroatoms.

In some of any of the embodiments described herein, P is aphotopolymerizable group, and in some embodiments, it is a UV-curablegroup, such that the curable material is photo-polymerizable or isUV-curable. In some embodiments, P is an acrylic polymerizable groupsuch as acrylate, methacrylate, acrylamide or methacrylamide, and suchcurable materials can be collectively represented by Formula A:

wherein at least one of R₁ and R₂ is and/or comprises a hydrocarbon, asdescribed herein.

The (═CH₂) group in Formula I represents a polymerizable group, and is,according to some embodiments, a UV-curable group, such that themono-functional curable material is a UV-curable material.

In some embodiments, R₁ is a carboxylate and R₂ is hydrogen, and thecompound is a mono-functional acrylate. In some embodiments, R₁ is acarboxylate and R₂ is methyl, and the compound is mono-functionalmethacrylate. Curable materials in which R₁ is carboxylate and R₂ ishydrogen or methyl are collectively referred to herein as“(meth)acrylates”.

In some of any of these embodiments, the carboxylate group isrepresented as —C(═O)—ORa, and Ra is a hydrocarbon as described herein.

In some embodiments, R₁ is amide and R₂ is hydrogen, and the compound isa mono-functional acrylamide. In some embodiments, R₁ is amide and R₂ ismethyl, and the compound is a mono-functional methacrylamide. Curablematerials in which R₁ is amide and R₂ is hydrogen or methyl arecollectively referred to herein as “(meth)acrylamide”.

In some of any of these embodiments, the amide group is represented as—C(═O)—NRbRa, and Ra and Rb are each independently selected fromhydrogen and hydrocarbon, at least one being a hydrocarbon as describedherein.

(Meth)acrylates and (meth)acrylamides are collectively referred toherein as (meth)acrylic materials.

When one or both of R₁ and R₂ comprise a polymeric or oligomeric moiety,the mono-functional curable compound of Formula A is an exemplarypolymeric or oligomeric mono-functional curable material, respectively.Otherwise, it is an exemplary monomeric mono-functional curablematerial.

Generally, the chemical composition of the hydrocarbon (R is the P—RFormula, or Ra/Rb, if present, in Formula A) determines if the curablematerial, and the hardened material formed thereof, is hydrophilic,hydrophobic or amphiphilic.

As used herein throughout, the term “hydrophilic” describes a physicalproperty of a material or a portion of a material (e.g., a chemicalgroup in a compound) which accounts for transient formation of bond(s)with water molecules, typically through hydrogen bonding.

Hydrophilic materials dissolve more readily in water than in oil orother hydrophobic solvents. Hydrophilic materials can be determined by,for example, as having Log P lower than 0.5, when Log P is determined inoctanol and water phases.

Hydrophilic materials can alternatively, or in addition, be determinedas featuring a lipophilicity/hydrophilicity balance (HLB), according tothe Davies method, of at least 10, or of at least 12.

As used herein throughout, the term “amphiphilic” describes a propertyof a material that combines both hydrophilicity, as described herein forhydrophilic materials, and hydrophobicity or lipophilicity, as definedherein for hydrophobic materials.

Amphiphilic materials typically comprise both hydrophilic groups asdefined herein and hydrophobic groups, as defined herein, and aresubstantially soluble in both water and a water-immiscible solvent(oil).

Amphiphilic materials can be determined by, for example, as having Log Pof 0.8 to 1.2, or of about 1, when Log P is determined in octanol andwater phases.

Amphiphilic materials can alternatively, or in addition, be determinedas featuring a lipophilicity/hydrophilicity balance (HLB), according tothe Davies method, of 3 to 12, or 3 to 9.

A hydrophilic material or portion of a material (e.g., a chemical groupin a compound) is one that is typically charge-polarized and capable ofhydrogen bonding.

Amphiphilic materials typically comprise one or more hydrophilic groups(e.g., a charge-polarized group), in addition to hydrophobic groups.

Hydrophilic materials or groups, and amphiphilic materials, typicallyinclude one or more electron-donating heteroatoms which form stronghydrogen bonds with water molecules.

Such heteroatoms include, but are not limited to, oxygen and nitrogen.Preferably, a ratio of the number of carbon atoms to a number ofheteroatoms in a hydrophilic materials or groups is 10:1 or lower, andcan be, for example, 8:1, more preferably 7:1, 6:1, 5:1 or 4:1, orlower. It is to be noted that hydrophilicity and amphiphilicity ofmaterials and groups may result also from a ratio between hydrophobicand hydrophilic moieties in the material or chemical group, and does notdepend solely on the above-indicated ratio.

A hydrophilic or amphiphilic material can have one or more hydrophilicgroups or moieties. Hydrophilic groups are typically polar groups,comprising one or more electron-donating heteroatoms such as oxygen andnitrogen.

Exemplary hydrophilic groups include, but are not limited to, anelectron-donating heteroatom, a carboxylate, a thiocarboxylate, oxo(═O), a linear amide, hydroxy, a (C1-4)alkoxy, an (C1-4)alcohol, aheteroalicyclic (e.g., having a ratio of carbon atoms to heteroatoms asdefined herein), a cyclic carboxylate such as lactone, a cyclic amidesuch as lactam, a carbamate, a thiocarbamate, a cyanurate, anisocyanurate, a thiocyanurate, urea, thiourea, an alkylene glycol (e.g.,ethylene glycol or propylene glycol), and a hydrophilic polymeric oroligomeric moiety, as these terms are defined hereinunder, and anycombinations thereof (e.g., a hydrophilic group that comprises two ormore of the indicated hydrophilic groups).

In some embodiments, the hydrophilic group is, or comprises, an electrondonating heteroatom, a carboxylate, a heteroalicyclic, an alkyleneglycol and/or a hydrophilic oligomeric moiety.

An amphiphilic moiety or group typically comprises one or morehydrophilic groups as described herein and one or more hydrophobicgroups, or, can a heteroatom-containing group or moiety in which theratio of number of carbon atoms to the number of heteroatoms accountsfor amphiphilicity.

A hydrophilic or amphiphilic mono-functional curable material accordingto some embodiments of the present invention can be a hydrophilicacrylate represented by Formula A1:

wherein R₁ and R₂ are as defined herein and at least one of R₁ and R₂ isand/or comprises a hydrophilic or amphiphilic moiety or group, asdefined herein.

In some of any of these embodiments, the carboxylate group, —C(═O)—ORa,comprises Ra which is a hydrophilic or amphiphilic moiety or group, asdefined herein. Exemplary Ra groups in the context of these embodimentsinclude, but are not limited to, heteroalicyclic groups (having a ratioof 10:1 or 8:1 or 6:1 or 5:1 or lower of carbon atoms toelectron-donating heteroatoms, such as morpholine, tetrahydrofurane,oxalidine, and the likes), hydroxyl, C(1-4)alkoxy, thiol, alkyleneglycol or a hydrophilic or amphiphilic polymeric or oligomeric moiety,as described herein. An exemplary hydrophilic monomeric mono-functionalacrylate is acryloyl morpholine (ACMO).

Exemplary hydrophilic or amphiphilic oligomeric mono-functional curablematerials include, but are not limited to, a mono-(meth)acrylatedurethane oligomer derivative of polyethylene glycol, amono-(meth)acrylated polyol oligomer, a mono-(meth)acrylated oligomerhaving hydrophilic substituents, a mono-(meth)acrylated polyethyleneglycol (e.g., methoxypolyethylene glycol), and a mono urethane acrylate.

In some embodiments, Ra in Formula A1 is or comprises a poly(alkyleneglycol), as defined herein.

In some embodiments, Ra in Formula A1 comprises both an amphiphilicgroup or moiety and a hydrophobic group or moiety, as described herein.Such materials are referred to herein as amphiphilic curable materialsthat comprise a hydrophobic moiety or group.

As used herein throughout, the term “hydrophobic” describes a physicalproperty of a material or a portion of a material (e.g., a chemicalgroup or moiety in a compound) which accounts for lack of transientformation of bond(s) with water molecules, and thus forwater-immiscibility, and is miscible or dissolvable in hydrocarbons.

A hydrophobic material or portion of a material (e.g., a chemical groupor moiety in a compound) is one that is typically non-charged or noncharge-polarized and does not tend to form hydrogen bonds.

Hydrophobic materials or groups typically include one or more of analkyl, cycloalkyl, aryl, alkaryl, alkene, alkynyl, and the like, whichare either un-substituted, or which, when substituted are substituted byone or more of alkyl, cycloalkyl, aryl, alkaryl, alkenyl, alkynyl, andthe like, or by other substituents, such as electron-donatingatom-containing substituents, yet a ratio of the number of carbon atomsto a number of heteroatoms in a hydrophobic materials or groups is atleast 10:1, and can be, for example, 12:1, more preferably 15:1, 16:1,18:1 or 20:1, or higher.

Hydrophobic materials dissolve more readily in oil than in water orother hydrophilic solvents. Hydrophobic materials can be determined by,for example, as having Log P higher than 1, when Log P is determined inoctanol and water phases.

Hydrophobic materials can alternatively, or in addition, be determinedas featuring a lipophilicity/hydrophilicity balance (HLB), according tothe Davies method, lower than 9, preferably lower than 6.

A h hydrophobic material can have one or more hydrophobic groups ormoieties that render the material hydrophobic. Such groups or moietiesare typically non-polar groups, as described hereinabove.

In some embodiments, the hydrophobic group or moiety is, or comprises, ahydrocarbon, as defined herein, preferably of at least 6 atoms, such asan alkylene chain of, for example, at least 6 carbon atoms in length.When the hydrocarbon is substituted or interrupted by heteroatoms orheteroatom-containing groups, the above-indicated ratio between thenumber of carbon atoms and heteroatoms applies.

A hydrophobic mono-functional curable material according to someembodiments of the present invention can be a hydrophobic acrylaterepresented by Formula A2:

wherein R₁ and R₂ are as defined herein and at least one of R₁ and R₂ isand/or comprises a hydrophobic group or moiety, as defined herein.

In some of any of these embodiments, the carboxylate group, —C(═O)—ORa,comprises Ra which is a hydrophobic group, as defined herein. Exemplaryhydrophobic monomeric mono-functional acrylates include isodecylacrylate, lauryl acrylate, stearyl acrylate, linolenyl acrylate,bisphenyl acrylate and the like.

In some embodiments, Ra in Formula A2 is or comprises an alkylene chainof at least 6 carbon atoms in length, preferably unsubstituted.

In some of any of the embodiments described herein, the mono-functionalcurable material comprises a hydrophobic mono-functional curablematerial.

In some of these embodiments, the hydrophobic mono-functional curablematerial is a hydrophobic mono-functional acrylate, which is alsoreferred to herein as “monofunctional acrylate type II”.

In some of any of the embodiments described herein, the mono-functionalcurable material comprises a hydrophilic or amphiphilic mono-functionalcurable material.

In some of any of the embodiments described herein, the mono-functionalcurable material comprises an amphiphilic mono-functional curablematerial.

In some of these embodiments, the amphiphilic mono-functional curablematerial is an amphiphilic mono-functional acrylate which does notcomprise a hydrophobic group as described herein, which is also referredto herein as “monofunctional acrylate type I”.

In some of any of the embodiments described herein, the mono-functionalcurable material comprises an amphiphilic mono-functional curablematerial which comprises a hydrophobic moiety or group as describedherein, which is also referred to herein as “monofunctional acrylatetype II”.

In some of any of the embodiments described herein, the mono-functionalcurable material comprises a combination of an amphiphilicmono-functional curable material and a hydrophobic mono-functionalcurable material (e.g., a combination of mono-functional acrylate oftype I and a mono-functional acrylate of type II).

In some of these embodiments, a weight ratio of the amphiphilicmono-functional curable material and the hydrophobic mono-functionalcurable material can range from 2:1 to 1:2, and preferably ranges from2:1 to 1:1 or from 1.5:1 to 1:1, or from 1.5:1 to 1.1:1, including anyintermediate values and subranges between any of the forgoing.

In some of any of the embodiments described herein, the mono-functionalcurable material comprises a combination of a hydrophobicmono-functional acrylate and an amphiphilic mono-functional acrylatewhich comprises a hydrophobic group as described herein (e.g., acombination of two mono-functional acrylate of type II).

In some of these embodiments, a weight ratio of the amphiphilicmono-functional curable material and the hydrophobic mono-functionalcurable material can range from 2:1 to 1:2, and preferably ranges from2:1 to 1:1 or from 1.5:1 to 1:1, or from 1.5:1 to 1.1:1, including anyintermediate values and subranges between any of the forgoing.

In some of any of the embodiments described herein, the mono-functionalcurable material comprises an amphiphilic mono-functional acrylate whichcomprises a hydrophobic group as described herein (e.g., amono-functional acrylate of type II).

In some of any of the embodiments described herein, the mono-functionalcurable material is such that features, when hardened, a Tg lower than0° C., preferably lower than −10° C., or lower than −20° C., or lower,e.g., ranging from −20 to −70° C. In cases where the mono-functionalcurable material comprises a combination of two or more materials, atleast one of these materials features, when hardened, a low Tg asdescribed herein, and optionally and preferably, all of the materialsfeature such a Tg.

Further embodiments of mono-functional curable materials are describedhereinbelow.

The Multi-Functional Curable Material:

As described herein, multi-functional curable materials are monomeric,oligomeric or polymeric curable materials featuring two or morepolymerizable groups. Such materials are also referred to herein ascross-linking agents.

According to some of any of the embodiments described herein, themulti-functional curable material is a di-functional curable material.Such materials provide for a low degree of cross-linking and therebyprovide for lower hardness of the hardened material.

According to some of any of the embodiments described herein, themulti-functional curable material features, when hardened, a Tg lowerthan −10, or lower than −20° C., and can be, for example, in a range offrom −10 to −70° C.

Exemplary multi-functional curable material according to someembodiments of the present invention can be represented by Formula B:

wherein:

-   -   each of R₃, R₄ and R₅ is independently hydrogen or a        C(1-4)alkyl;    -   L₁ is a linking moiety, a branching unit or moiety (in case n is        greater than 1) or absent;    -   L₂ is a linking moiety, a branching unit or moiety (in case k is        other than 0) or is absent;    -   L₃ is a linking moiety, a branching unit or moiety (in case m is        greater than 1) or absent;    -   each of P₁ and P₂ is independently a hydrocarbon, or an        oligomeric or polymeric group or moiety, as there terms are        defined herein, or absent;    -   each of X1, X₂ and X₃ is independently a carboxylate, an amide,        or absent; and    -   each of n, m and k is 0, 1, 2, 3 or 4,    -   provided that n+m+k is at least 2.

Multi-functional curable materials of Formula II in which one, two orall of X₁, X₂ and X₃, when present, is a carboxylate, aremulti-functional acrylates. When one or more of R₃, R₄ and R₅, whenpresent, is methyl, the curable materials are multi-functionalmethacrylates.

Multifunctional curable materials in which one, two or all of X₁, X₂ andX₃, when present, is carboxylate, can include a combination of acrylateand methacrylate functional moieties.

In some embodiments, the acrylate or methacrylate multifunctionalcurable material is monomeric, such that none of P₁ and P₂ is apolymeric or oligomeric moiety. In some of these embodiments, one orboth of P₁ and P₂ is a hydrophilic or amphiphilic group as describedherein, for example, an alkylene glycol, or any other hydrophilic oramphiphilic linking group, or is a short chain (e.g., of 1-6 carbonatoms), substituted or unsubstituted hydrocarbon moiety, as definedherein.

In some embodiments, one or both of P₁ and P₂ is a polymeric oroligomeric moiety as defined herein, and the curable compound is anoligomeric multi-functional curable material, for example, an oligomericmulti-functional acrylate or methacrylate, as described herein for X₁,X₂ and/or X₃. If both P₁ and P₂ are present, L₂ can be, for example, alinking moiety such as a hydrocarbon, comprising alkyl, cycloalkyl, aryland any combination thereof. Exemplary such curable materials includeethoxylated or methoxylated polyethylene glycol diacrylate, andethoxylated bisphenol A diacrylate.

Other non-limiting examples include polyethylene glycol diacrylate,polyethylene glycol dimethacrylate, polyethylene glycol-polyethyleneglycol urethane diacrylate, an acrylated oligourethane, and a partiallyacrylated polyol oligomer.

In some embodiments, one or more of P₁ and P₂ is, or comprises, apoly(alkylene glycol) moiety, as defined herein.

Exemplary multi-functional acrylates are described in the Examplessection that follows.

In some of any of the embodiments described herein, the mono-functionalcurable material(s) and the multi-functional curable material(s) arecurable when exposed to the same curing condition.

In some embodiments, the mono-functional curable material(s) and themulti-functional curable material(s) are both photopolymerizable and insome embodiments are both UV-curable.

In some embodiments, the mono-functional curable material(s) and themulti-functional curable material(s) are both acrylic compounds, and insome embodiments are both (meth)acrylates or both are acrylates.

Initiators:

In some of any of the embodiments described herein, the soft modelingmaterial formulation further comprises one or more agents which promotethe polymerization of the curable materials, and are referred to hereinas initiators.

In some of any of the embodiments described herein, the curablematerials as described herein and an initiator form together a curablesystem. Such a system can further comprise an inhibitor, as describedhereinafter.

It is to be noted that compounds/agents that form a part of a curablesystem, even if not curable by themselves, are not considered herein asnon-curable materials, let alone non-curable polymeric materials asdescribed herein.

In some of any of the embodiments described herein, a “curable system”comprises one or more curable materials and optionally one or moreinitiators and/or catalysts for initiating curing of the curablematerials, and, further optionally, one or more conditions (alsoreferred to herein as curing conditions) for inducing the curing, asdescribed herein.

The one or more initiators are selected in accordance with the selectedcurable materials. Typically, initiators are further selected inaccordance with the polymerization type of the curable materials. Forexample, a free radical initiator is selected for initiatingfree-radical polymerization (e.g., as in the case of acrylic curablematerials); cationic initiator is selected for initiating cationicpolymerization, and so forth. Further, photoinitiators are used in caseone or more of the curable materials is photopolymerizable.

In some of any of the embodiments described herein, the curable systemis a photocurable system, and the initiator is a photoinitiator.

In some embodiments, the curable system comprises acrylic compounds andthe photoinitiator is a free-radical photoinitiator.

A free-radical photoinitiator may be any compound that produces a freeradical on exposure to radiation such as ultraviolet or visibleradiation and thereby initiates a polymerization reaction. Non-limitingexamples of suitable photoinitiators include benzophenones (aromaticketones) such as benzophenone, methyl benzophenone, Michler's ketone andxanthones; acylphosphine oxide type photo-initiators such as2,4,6-trimethylbenzolydiphenyl phosphine oxide (TMPO),2,4,6-trimethylbenzoylethoxyphenyl phosphine oxide (TEPO), andbisacylphosphine oxides (BAPO's); benzoins and bezoin alkyl ethers suchas benzoin, benzoin methyl ether and benzoin isopropyl ether and thelike. Examples of photoinitiators are alpha-amino ketone, andbisacylphosphine oxide (BAPO's). Further examples includephotoinitiators of the Irgacure® family.

A free-radical photo-initiator may be used alone or in combination witha co-initiator. Co-initiators are used with initiators that need asecond molecule to produce a radical that is active in the photocurablefree-radical systems. Benzophenone is an example of a photoinitiatorthat requires a second molecule, such as an amine, to produce a freeradical. After absorbing radiation, benzophenone reacts with a ternaryamine by hydrogen abstraction, to generate an alpha-amino radical whichinitiates polymerization of acrylates. Non-limiting example of a classof co-initiators are alkanolamines such as triethylamine,methyldiethanolamine and triethanolamine.

In some of any of the embodiments described herein, the modelingmaterial formulations comprises a free-radical curable system, andfurther comprises a radical inhibitor, for preventing or slowing downpolymerization and/or curing prior to exposing to the curing condition.

In some of any of the embodiments described herein, the curable systempolymerizable or cured via cationic polymerization, and are referred toherein also as cationic polymerizable or cationic curable systems.

In some embodiments, a cationic polymerizable material is polymerizableor curable by exposure to radiation. Systems comprising such a materialcan be referred to as photo-polymerizable cationic systems, orphotoactivatable cationic systems.

In some embodiments, a cationic curable system further comprises acationic initiator, which produces cations for initiating thepolymerization and/or curing.

In some embodiments, the initiator is a cationic photoinitiator, whichproduces cations when exposed to radiation.

Suitable cationic photoinitiators include, for example, compounds whichform aprotic acids or Bronsted acids upon exposure to ultraviolet and/orvisible light sufficient to initiate polymerization. The photoinitiatorused may be a single compound, a mixture of two or more activecompounds, or a combination of two or more different compounds, i.e.co-initiators. Non-limiting examples of suitable cationicphotoinitiators include aryldiazonium salts, diaryliodonium salts,triarylsulphonium salts, triarylselenonium salts and the like. Anexemplary cationic photoinitiator is a mixture of triarylsolfoniumhexafluoroantimonate salts.

Non-limiting examples of suitable cationic photoinitiators includeP-(octyloxyphenyl) phenyliodonium hexafluoroantimonate UVACURE 1600 fromCytec Company (USA), iodonium(4-methylphenyl)(4-(2-methylpropyl)phenyl)-hexafluorophosphate known asIrgacure 250 or Irgacure 270 available from Ciba Speciality Chemicals(Switzerland), mixed arylsulfonium hexafluoroantimonate salts known asUVI 6976 and 6992 available from Lambson Fine Chemicals (England),diaryliodonium hexafluoroantimonate known as PC 2506 available fromPolyset Company (USA), (tolylcumyl) iodonium tetrakis(pentafluorophenyl) borate known as Rhodorsil® Photoinitiator 2074available from Bluestar Silicones (USA), iodoniumbis(4-dodecylphenyl)-(OC-6-11)-hexafluoro antimonate known as Tego PC1466 from Evonik Industries AG (Germany).

In some of any of the embodiments described herein, an amount of aninitiator (e.g., free-radical photoinitiator) ranges from 1 to 5, orfrom 1 to 3, weight percents, including any intermediate values andsubranges therebetween. In exemplary embodiments, a combination of twoor more initiators (e.g., photoinitiators) is used, and an amount ofeach ranges from 1 to 3, weight percents.

Additional Components:

According to some of any of the embodiments described herein, the softmodeling material formulation further comprises additional, non-curablecomponents, such as, for example, inhibitors, surfactants, dispersants,colorants (coloring agents), stabilizers, and the like. Commonly usedsurfactants, dispersants, colorants and stabilizers are contemplated.Exemplary concentrations of each component, if present, range from about0.01 to about 1, or from about 0.01 to about 0.5, or from about 0.01 toabout 0.1, weight percents, of the total weight of the formulationcontaining same. Exemplary components are described hereinafter.

In some of any of the embodiments described herein, the formulationcomprises a curing inhibitor, that is, an agent that inhibits or reducesan amount of the curing in the absence of a curing condition. In someembodiments, the inhibitor is a free radical polymerization inhibitor.In some embodiments, an amount of an inhibitor (e.g., a free radicalinhibitor) ranges from 0.01 to 2, or from 1 to 2, or from 0.05 to 0.15,or is 0.1, weight percent, including any intermediate values andsubranges therebetween, depending on the type of inhibitor used.Commonly used inhibitors, such as radical inhibitors, are contemplated.

In exemplary embodiments, a free radical inhibitor such as NPAL, orequivalents thereof, is used in an amount of from 0.01 to 1, or from0.05 to 0.2, or from 0.05 to 0.15, or is 0.1, weight percent.

In alternative embodiments, a free radical inhibitor that is devoid ofnitro or nitroso groups is employed. Exemplary such inhibitors are thoseof the Genorad™ family (e.g., Genorad18).

In exemplary embodiments, such a free radical inhibitor is used in anamount of from 0.1 to 3, or from 0.1 to 2, or from 0.5 to 2, or from 1to 1.5, weight percents, including any intermediate values and subrangestherebetween.

In exemplary embodiments, the soft modeling material formulationcomprises a surfactant. Exemplary surfactants are those marketed as BYKsurface additives. In some embodiments, the surfactant is a curablematerial, preferably curable upon exposure to the same curing conditionas the curable materials in the formulation. In some embodiments, thesurfactant is a UV-curable surfactant, and in some embodiments, thesurfactant is a UV-curable BYK surfactant (e.g., BYK UV-3150 or BYKUV-3500).

In some embodiments, an amount of the surfactant in the formulationranges from 0.1 to 1%, by weight, as described herein.

Exemplary Soft Modeling Formulations:

In some of any of the embodiments described herein, the soft modelingmaterial formulation comprises non-curable polymeric material(s) asdescribed herein, and an acrylic curable system which comprises amono-functional acrylate (e.g., a combination of an amphiphilic and ahydrophobic mono-functional acrylate), a free-radical photoinitiator andoptionally a free-radical inhibitor.

In some embodiments, the formulation further comprises one or more ofthe additional components as described herein.

In some embodiments, the formulation further comprises a coloring agent,as described herein, for example, such that provides a red tint,flesh-like color to the formulations, or a skin or skin pigmentationtint, to the formulations and objects or portions thereof made thereof.Exemplary flesh-like colors that are suitable for use with acrylicmaterials include, without limitation, those manufactured by ProstheticResearch Specialists, Inc. as “Flesh color system”; and color pigmentsmarketed by Kingsley Mfg. Co.

In some embodiments, a concentration of the coloring depends on theintended use of the formulation and the desired visual properties of theobject, and can range from 0.01 to 5, or from 0.01 to 1, or from 0.1 to1, including any intermediate values and subranges tehrebteween.

In some of any of the embodiments described herein, the soft modelingmaterial formulation comprises:

-   -   a mono-functional amphiphilic acrylate, as described herein in        any of the respective embodiments, in an amount of 25-35 weight        percents;    -   a mono-functional hydrophobic acrylate, as described herein in        any of the respective embodiments, in an amount of 25-30 weight        percents;    -   a multi-functional acrylate, as described herein in any of the        respective embodiments, in an amount of 5-10 weight percents;        and    -   a non-curable polymeric material featuring a molecular weight of        at least 1000, or at least 1500 or at least 2000 Daltons; and a        Tg lower than 0, or lower than −10, or lower than −20, ° C., as        described herein in any of the respective embodiments, in an        amount of 30-35 weight percents.

In some of these embodiments, the non-curable polymeric materialcomprises a polypropylene glycol and/or a block co-polymer comprising atleast one polypropylene glycol block, each featuring a molecular weightof at least 2000 Daltons, as described herein in any of the respectiveembodiments.

In some of these embodiments, the multi-functional acrylate is adi-functional acrylate, and in some embodiments it is a urethanediacrylate.

In some of these embodiments, the mono-functional amphiphilic acrylatecomprises a hydrocarbon chain of at least 6 carbon atoms and at least 2alkylene glycol groups.

In some of these embodiments, the mono-functional hydrophobic acrylatecomprises a hydrocarbon chain of at least 8 carbon atoms.

Exemplary formulations are presented hereinunder.

According to some of any of the embodiments described herein, theuncured building material comprises two or more soft modeling materialformulations as described herein, each comprising a differentcombination of curable and non-curable materials according to thepresent embodiments, and optionally each feature, when hardened, adifferent Shore A hardness values in the range of 1-10 and/or differentShore 00 hardness values in the range of 0-40.

In some embodiments, such two of more building material formulationsrepresent a formulation system of a soft modeling formulation.

Table 1.1 below presents exemplary formulations according to the presentembodiments, which exhibit Shore scale A hardness 0 or Shore 00 hardnessof from 0 to about 40, as described herein.

The phrase “monofunctional acrylate type I” as used in Table 1.1,encompasses monofunctional hydrophilic or hydrophilic amphiphilicacrylates, more specifically one or more monomeric, oligomeric orpolymeric curable material(s) featuring an acrylate group as apolymerizable group and one or more heteroatoms (e.g., O, N or both) orheteroatom-containing groups (e.g., carboxylate, amide, alkylene glycoland combinations thereof) which impart a hydrophilic or amphiphilicnature. See also Formula A1 wherein R₁ is C(═O)—O—Ra, and Ra is ahydrophilic or amphiphilic moiety that does not include a hydrophobicgroup or moiety as described herein. Exemplary materials includealkoxy-terminated poly(ethylene glycol) acrylates (e.g., such asmarketed as AM130); urethane acrylates (e.g., such as marketed asGenomer®, for example, Genomer 1122); Acryloyl morpholine, and any ofthe other respective curable materials described herein.

The phrase “monofunctional acrylate type II” encompasses one or moremonomeric, oligomeric or polymeric, preferably monomeric, hydrophobic orhydrophobic amphiphilic, curable material(s) featuring an acrylate groupas a polymerizable group and at least one hydrophobic moiety or group,e.g., a hydrocarbon of at least 6 carbon atoms in length, as definedherein. See also Formula A2 wherein R₁ is C(═O)—O—Ra, and Ra is orcomprises a hydrophobic moiety or group.

Exemplary such materials include compounds of Formula A1 as describedherein featuring as Ra groups such as nonyl phenyl, isodecyl, and/orlauryl groups, optionally in combination with alkylene glycol groups,for example, those marketed by Sartomer as SR395; SR504D, SR335, SR7095and more.

The phrase “non-curable polymeric material” as used in the Examplessection herein encompasses one or more polymeric material(s), preferablyamphiphilic, devoid of a polymerizable acrylate group or any otherpolymerizable group that participates in polymerization upon exposure toconditions that initiate acrylate polyhmerization (e.g., devoid ofphotopolymerizable group or a group that polyhmerizes upon exposure toradiation at wavelength that induce acrylate polymerization).Preferably, the non-curable polymeric material(s) include one or moreblock co-polymers of PEG and PPG, also known under the Trade name“Pluronic®”, at any order and number of blocks, at any MW and featuringa variety of Tg values when hardened. Preferably, the non-curablepolymeric material(s) include one or more block co-polymers of PEG andPPG such as PEG-PPG-PEG and PPG-PEG-PPG, featuring no more than 10% byweight of PEG, and/or a PEG/PPG ratio as described herein, featuring MWof at least 500, preferably at least 900 and more preferably of at least2,000, Daltons and/or featuring, when hardened, Tg lower than 20,preferably lower than 0, more preferably lower than −20, ° C.Preferably, these materials are characterized by low solubility (e.g.,lower than 20% or lower than 10%, or lower), or insolubility in water.

The phrase “multi-functional acrylate” as used in the Examples sectionherein encompasses one or more monomeric, oligomeric or polymericcurable material(s) featuring two or more polymerizable acrylate groups.Such materials are also referred to herein as cross-linking agents.Exemplary such materials include, but are not limited to, urethanediacrylates such as, for example, marketed as Ebecryl 230; aliphaticdi-, tri- or tetra-acrylates such as, for example, trimethylolpropanetriacrylate, optionally ethoxylated (e.g., materials marketed asPhotomer 4072, Photomer 4158, Photomer 4149, Photomer 4006, MiramerM360, SR499), glyceryl triacrylate, pentaerythritol tetraacrylate,optionally ethoxylated (e.g., marketed as Photomer 4172), heaxnedioldiacrylate, PEGDA, and more; epoxy diacrylates such as marketed asPhotomer 3005, Photomer 3015, Photomer 3016, Pgotomer 3316. Preferably,the multi-functional acrylate features, when hardened, Tg lower than 20°C., or lower than 0° C., or lower.

The phrase “polysiloxane” encompasses non-curable organic and inorganicmaterials comprising a polysiloxane backbone, including, as non-limitingexamples, PDMS and derivatives thereof and block-copolymers containingsame.

The terms “photoinitiator” and “inhibitor” are as defined herein.

All formulations presented in Table 1.1 comprise one or morephotoinitiators in an amount ranging for 1 to 5% by weight (e.g., 3%wt.).

Exemplary photoinitiators include those of the Irgacure® family, forexample, 1819, 1184, and a combination thereof.

All formulations presented in Table 1.1 comprise one or more inhibitors(free-radical polymerization inhibitors) in an amount ranging for 0.01to 1% by weight (e.g., 0.1% wt.), unless otherwise indicated. Exemplaryinhibitors include Tris(N-nitroso-N-phenylhydroxylamine) Aluminum Salt(NPAL) and inhibitors of the Genorad™ family, such as, for example, G18.

Some of the formulations presented in Table 1.1 further compriseadditional, non-reactive components (additives) as described herein.

In an exemplary formulation (BM219) a UV-curable surface active agent isused—BYK UV-3500—Polyether-modified, acryl-functionalpolydimethylsiloxane.

TABLE 1.1 Monofunctional Monofunctional Non-curable Formulation acrylateType 1 Acrylate Type II Multi-functional polymeric material Code (% wt.)(% wt.) acrylate* (% wt.) (% wt.) BM19 X  40  7 50^(a) BM19(5) 5 40^(d) 7 45^(a) BM19(10) 10 40^(d)  7 40^(a) BM29 X 52^(e) 15 30^(a) BM32 X40^(f)  7 50^(a) BM35 X 50^(e)  7 40^(a) BM38 10 50^(e)  7 30^(a) BM43 X57 (27^(e) + 30^(d)) 10 30^(a) BM44 X 57 (15^(e) + 42^(d)) 10 30^(a)BM58 20 30^(d)  7 40^(a) BM61 X 57 (27^(e) + 30^(d))  7 33^(c) BM62 X 57(27^(e) + 30^(d))  7 33^(b) BM62 X 57 (27^(f) + 30^(d))  7 33^(a) BM6410 50^(f)  7 30^(c) BM66 X 57 (15^(d) + 42^(e))  3 33^(c) BM67 20.931.3^(d)  3 41.8^(a) BM68 18.2 27.3^(d) 15 36.5^(a) BM75 X 94^(d)  3 XBM76 X 87^(d)  3 7^(c) BM77 X 79^(d)  3 15^(c) BM78 X 64^(d)  3 30^(c)BM101 X 61 (34^(d)+27^(e))   3** 33^(c) BM102 X 61 (34^(d)+27^(e))   3*** 33^(c) BM103 27 33^(d)  7 30^(b) BM104 60 X  7 30^(b) BM108 X 57(27^(e) + 30^(d))  7 33^(h) BM109 X 67 (27^(e) + 40^(d))  7 23^(c) BM110X 47 (27^(e) + 20^(d))  7 43^(c) BM111 X 67 (37^(e) + 30^(d))  7 23^(c)BM112 X 62 (27^(e) + 35^(d))  7 28^(c) BM131 X 57 (27^(e) + 30^(d))  733^(g) BM151 X 57 (27^(e) + 30^(d))  7 33 (16.5^(g) + 16.5^(c))BM205.4^(#) X 56 (27^(e) + 29^(d))  7 33^(k) BM219^(##) X 63^(f)  7 26(13^(g) + 13^(c)) (Table 1.1; Cont.) ^(a)= PPG; MW 900 ^(b)= PEG-PPG-PEGblock copolymer MW 2750 ^(c)= PPG; MW 2000 ^(h)= PPG-PEG-PPG blockcopolymer MW 3500 ^(g)= PPG-PEG-PPG block copolymer MW 3250 ^(k)=PEG-PPG-PEG block copolymer MW 2000 ^(d)= ethoxylated nonylphenylacrylate ^(e)= isodecyl acrylate ^(f)= lauryl acrylate or ethoxylatedlauryl acrylate *= urethane diacrylate (e.g., Ebecryl 230) unlessotherwise indicated **= aliphatic triacrylate (e.g., trimetholopropanetriacrylate) ***= epoxy diacrylate (e.g., Photomer 3005F) ^(#)= G18 typeinhibitor used, at a concentration of 1.5% wt. + UV curable surfaceactive agent (e.g., BYK3500) ^(##)= G18 type inhibitor used, at aconcentration of 1% wt.

Additional exemplary formulations, comprising a multi-functionalacrylate other than urethane diacrylate and/or at an amount of from 1 to3% wt., and/or comprising polysiloxane compounds at an amount of 5-10%wt., have been prepared, and all featured Shore A hardness 0.

Example 2 Liquid Material Formulation

A building material formulation that provides, upon exposure to a curingcondition, a liquid or liquid-like material is also referred to hereinas a liquid building material formulation or a liquid materialformulation, or a liquid formulation or as formulation L. In someembodiments, such a formulation is intended to remain liquid or form aliquid-like material upon being dispensed and exposed to a curingcondition.

According to embodiments of the present invention Formulation L is suchthat provides a liquid or liquid-like material, as defined herein.

The liquid building material formulation can comprise one or moreformulations, each comprising one or more non-curable materials in anamount of at least 50%, preferably at least 60%, or at least 70%, or atleast 80%, or at least 90%, or 100%, by weight, of the total weight ofthe second building material formulation.

Because the liquid material formulation is comprised mainly ofnon-curable materials, when it is exposed to a curing condition, itundergoes minimal or essentially null hardening (e.g., no more than 20%,or no more than 10% by weight, of the material, hardens, e.g.,polymerizes), thus maintaining essentially the same fluidity, orviscosity, as that of the dispensed formulation, such that the materialobtained upon exposure to a curing condition is a liquid or liquid-likematerial, as defined herein.

In some of any of the embodiments described herein, one or moreformulations in the liquid material building formulations are such thatupon exposure to a curing condition provide a liquid or liquid-likematerial that features a viscosity of no more than 10,000 centipoises,or of no more than 1,000 centipoises, or of no more than 100centipoises, for example, of 10-50 centipoises.

In some of any of the embodiments described herein, the liquid buildingmaterial formulation (formulation L) feature(s) a viscosity which isdifferent from the viscosity of the liquid or liquid-like material(Material L) by no more than 20%, preferably by no more than 10%. Thus,a change in the viscosity or the fluidity of the liquid buildingmaterial formulation upon exposure to a curing condition is minimal(e.g., no more than 10%) or even null.

In some of any of the embodiments described herein for the liquidbuilding material formulation, the non-curable material is or comprisesa polymeric material and in some embodiments the polymeric material isor comprises one or more amphiphilic and/or hydrophilic polymer(s).

In some of any of the embodiments described herein for the liquidbuilding material formulation, the non-curable material is or comprisesa poly(alkylene glycol), as defined herein. The non-curable material canbe a poly(alkylene glycol) per se or can comprise one or morepoly(alkylene glycol) chains or blocks.

In some of any of the embodiments described herein, the non-curablematerial comprises a poly(alkylene glycol) having a molecular weight ofless than 2000 grams/mol, and in some embodiments, the poly(alkyleneglycol) is a polymer having a molecular weight of from 200 to 2000 orfrom 200 to 1000 or from 200 to 800 or from 200 to 600, or of 400,grams/mol.

In some of any of the embodiments described herein, the poly(alkyleneglycol) is a poly(ethylene glycol). Alternatively, it is apoly(propylene glycol).

Other non-curable materials suitable for inclusion in the liquidbuilding material formulation, instead of or in addition to apoly(alkylene glycol) as described herein, include, but are not limitedto, block co-polymers comprising one or more poly(alkylene glycol)blocks, for example, block-co-polymers of poly(ethylene glycol) andpoly(propylene glycol), such as those marketed under the trade namePluronic®, polyols such as diols (e.g., propanediol), glycerols, andhigher polyols.

Additional non-curable materials suitable for inclusion in the liquidformulation, formulation L, include one or more oils, such as, but notlimited to, one or more of a vegetable oil, a synthetic oil, ahydrocarbon oil, a silicone oil, a fatty acid, a mineral oil, and aparaffin oil. In some embodiments, the oil features a viscosity or anyof the properties described herein as characterizing Material L.

In some of any of the embodiments described herein, the liquid buildingformulation further comprises water.

In some of any of the embodiments described herein, the liquid buildingformulation comprises a curable material, optionally in combination witha non-curable material, but is devoid of a catalyst or initiator thatprompts the curing (e.g., polymerization) of the curable material. Insuch embodiments, the hardening of the liquid building formulation uponexposure to a curing condition is minimized or nullified, and the formedliquid or liquid-like material features fluidity properties that aresimilar to that of the liquid building formulation, as described herein.

In some of any of the embodiments described herein, the liquid material(material L) features a shear modulus of less than 20 kPa, or of lessthan 15 kPa, or of less than 10 kPa, or of less than 5 kPa, thusfeaturing a consistency of a very soft and flowable gel. Formulationsproviding such a material are also referred to herein as formulationsthat provide a liquid-like material.

In some of these embodiments, the liquid building material formulationcomprises a curable material, optionally and preferably in combinationwith a non-curable material, as described herein in any of therespective embodiments.

According to some of these embodiments, the curable material is orcomprises a mono-functional curable material, as defined herein.

Preferably, the curable material is in an amount of no more than 50%,preferably no more than 40%, or no more than 30%, or no more than 20%,and even of 15%, 10%, by weight, or less, of the total weight of theliquid material formulation. In some embodiments, an amount of thecurable material in the liquid building material formulation ranges from10 to 25 weight percents.

According to some of any of the embodiments described herein, thecurable material is amphiphilic or hydrophilic (e.g., as described inExample 1 herein).

According to some of any of the embodiments described herein, thecurable material is such that when hardened, it provides a water-solubleor water-miscible material, as defined herein.

According to some of any of the embodiments described herein, thecurable material is such that when hardened, it provides ashear-thinning and/or thixotropic and/or thermal-thinning material, asdefined herein.

Exemplary liquid building material formulations include formulationscomprising a poly(alkylene glycol) as described herein, in an amount ofat least 50% and up to 100%, by weight, optionally in combination withone or more curable materials as described herein, in a total amount offrom 10 to 25% by weight, and further optionally in combination withadditional components as described herein.

Exemplary liquid formulations L include formulations comprising one ormore oils, as described herein, in an amount of at least 50% and up to100%, by weight, optionally in combination with one or more curablematerials as described herein, in a total amount of from 10 to 25% byweight, and further optionally in combination with additional componentsas described herein.

Generally, in some embodiments, the liquid building material formulationis selected such that the liquid or liquid-like material iswater-soluble or water-miscible, as defined herein.

In some embodiments, the liquid material is water-miscible and aliquid-like material is water-soluble.

Generally, in some embodiments, the liquid building material formulationis selected such that the liquid or liquid-like material (Material L) isa shear-thinning material, as defined herein.

Generally, in some embodiments, the liquid building material formulationis selected such that the liquid or liquid-like material (Material L) isa thixotropic material, as defined herein.

Generally, in some embodiments, the liquid building material formulationis selected such that the liquid or liquid-like material (Material L) isa thermal-thinning material, as defined herein.

In some of any of the embodiments described herein, the uncured buildingmaterial comprises two or more liquid building material formulations, asdescribed herein, for example, one or more formulations which provide aliquid material, featuring a viscosity which is substantially the sameas that of the uncured formulation, as described herein, and comprisinga non-curable material, and one or more formulations which provide aliquid-like material, featuring a shear stress of no more than 20 kPa,as described herein, and comprising curable and non-curable materials,as described herein.

In some of these embodiments, the dispensing is such that small hollowstructures, featuring at least one dimension at the millimeter scale, asdefined herein, are filled with a formulation that provides a liquidmaterial, and larger hollow structures are filled with a formulationthat provides a liquid-like material.

When the liquid building material formulation described in this exampleis dispensed, and straightened, the AM system, for example, by means ofthe controller, optionally and preferably ensures that the newlydispensed layer is in a still-air environment.

As used herein, “still-air environment” refers to an environment inwhich there is no air flow, or in which an air flows at speed less than3 m/s.

Example 3 Elastomeric Curable Material

Herein throughout, the phrase “elastomeric curable formulation” is alsoreferred to herein as “elastomeric modeling material formulation”,“elastomeric modeling formulation” or simply as “elastomericformulation”, and describes a formulation which, when hardened, featuresproperties of a rubber or rubbery-like materials, also referred toherein and in the art as elastomers.

Elastomers, or rubbers, are flexible materials that are characterized bylow Tg (e.g., lower than room temperature, preferably lower than 10° C.,lower than 0° C. and even lower than −10° C.).

Exemplary such formulations are those marketed as Tango™, Tango+™ andAgilus™ families (e.g., Agilus™ 30).

Exemplary such formulations are described in WO2017/208238, which isincorporated by reference as if fully set forth herein.

Whenever “Agilus” or “Agilus formulation” is indicated, it is meant aformulation of the Agilus™ family (e.g., a formulation as described inWO2017/208238), optionally and preferably Agilus™ 30.

According to some of any of the embodiments described herein, theelastomeric curable modeling formulation comprises at least oneelastomeric curable material.

The phrase “elastomeric curable material” describes a curable material,as defined herein, which, upon exposure to curing energy, provides acured material featuring properties of an elastomer (a rubber, orrubber-like material).

Elastomeric curable materials typically comprise one or morepolymerizable (curable) groups, which undergo polymerization uponexposure to a suitable curing condition (e.g., curing energy), linked toa moiety that confers elasticity to the polymerized and/or cross-linkedmaterial. Such moieties typically comprise alkyl, alkylene chains,hydrocarbon, alkylene glycol groups or chains (e.g., oligo orpoly(alkylene glycol) as defined herein, urethane, oligourethane orpolyurethane moieties, as defined herein, and the like, including anycombination of the foregoing, and are also referred to herein as“elastomeric moieties”.

An elastomeric curable material can be a mono-functional ormulti-functional material, or a combination thereof.

An elastomeric mono-functional curable material according to someembodiments of the present invention can be a vinyl-containing compoundrepresented by Formula I:

wherein at least one of R₁ and R₂ in Formula I is and/or comprises anelastomeric moiety, as described herein.

The (═CH₂) group in Formula I represents a polymerizable group, and is,according to some embodiments, a UV-curable group, such that theelastomeric curable material is a UV-curable material.

For example, R₁ in Formula I is or comprises an elastomeric moiety asdefined herein and R₂ is, for example, hydrogen, C(1-4) alkyl, C(1-4)alkoxy, or any other substituent, as long as it does not interfere withthe elastomeric properties of the cured material.

In some embodiments, R₁ in Formula I is a carboxylate as describedherein, R₂ is hydrogen, and the compound is a mono-functional acrylatemonomer. In some embodiments, R₁ in Formula I is a carboxylate asdescribed herein, and R₂ is methyl, and the compound is mono-functionalmethacrylate monomer. Curable materials in which R₁ is carboxylate andR₂ is hydrogen or methyl are collectively referred to herein as“(meth)acrylates”.

In some of any of these embodiments, the carboxylate group isrepresented by —C(═O)—ORc, and Rc is an elastomeric moiety as describedherein.

In some embodiments, R₁ in Formula I is amide as described herein, R₂ ishydrogen, and the compound is a mono-functional acrylamide monomer. Insome embodiments, R₁ in Formula I is amide as described herein, R₂ ismethyl, and the compound is mono-functional methacrylamide monomer.Curable materials in which R₁ is amide and R₂ is hydrogen or methyl arecollectively referred to herein as “(meth)acrylamide”.

(Meth)acrylates and (meth)acrylamides are collectively referred toherein as (meth)acrylic materials.

In some embodiments, the amide is presented by —C(═O)—NRdRe, and Rd andRe are selected from hydrogen and an elastomeric moiety, at least onebeing an elastomeric moiety, as defined herein. When one or both of R₁and R₂ in Formula I comprise a polymeric or oligomeric moiety, themono-functional curable compound of Formula I is an exemplary polymericor oligomeric mono-functional curable material. Otherwise, it is anexemplary monomeric mono-functional curable material.

In multi-functional elastomeric materials, the two or more polymerizablegroups are linked to one another via an elastomeric moiety, as describedherein.

In some embodiments, a multifunctional elastomeric material can berepresented by Formula I as described herein, in which R₁ comprises anelastomeric material that terminates by a polymerizable group, asdescribed herein.

For example, a di-functional elastomeric curable material can berepresented by Formula I*:

wherein E is an elastomeric linking moiety as described herein, and R′₂is as defined herein for R₂ in Formula I.

In another example, a tri-functional elastomeric curable material can berepresented by Formula II:

wherein E is an elastomeric linking moiety as described herein, and R′₂and R″₂ are each independently as defined herein for R₂ in Formula I.

In some embodiments, a multi-functional (e.g., di-functional,tri-functional or higher) elastomeric curable material can becollectively represented by Formula III:

Wherein:

-   -   R₂ and R′₂ are as defined herein;    -   B is a di-functional or tri-functional branching unit as defined        herein (depending on the nature of X₁);    -   X₂ and X₃ are each independently absent, an elastomeric moiety        as described herein, or is selected from an alkyl, a        hydrocarbon, an alkylene chain, a cycloalkyl, an aryl, an        alkylene glycol, a urethane moiety, and any combination thereof;        and    -   X₁ is absent or is selected from an alkyl, a hydrocarbon, an        alkylene chain, a cycloalkyl, an aryl, an alkylene glycol, a        urethane moiety, and an elastomeric moiety, each being        optionally being substituted (e.g., terminated) by a        meth(acrylate) moiety (O—C(═O)CR″₂═CH₂), and any combination        thereof, or, alternatively, X₁ is:

wherein:

-   -   the curved line represents the attachment point;    -   B′ is a branching unit, being the same as, or different from, B;    -   X′₂ and X′₃ are each independently as defined herein for X₂ and        X₃; and    -   R″₂ and R′″₂ are as defined herein for R₂ and R′₂.    -   provided that at least one of X₁, X₂ and X₃ is or comprises an        elastomeric moiety as described herein.

The term “branching unit” as used herein throughout describes amulti-radical, preferably aliphatic or alicyclic, linking moiety. By“multi-radical” it is meant that the linking moiety has two or moreattachment points such that it links between two or more atoms and/orgroups or moieties.

That is, the branching unit is a chemical moiety that, when attached toa single position, group or atom of a substance, creates two or morefunctional groups that are linked to this single position, group oratom, and thus “branches” a single functionality into two or morefunctionalities.

In some embodiments, the branching unit is derived from a chemicalmoiety that has two, three or more functional groups. In someembodiments, the branching unit is a branched alkyl or a branchedlinking moiety as described herein.

Multi-functional elastomeric curable materials featuring 4 or morepolymerizable groups are also contemplated, and can feature structuressimilar to those presented in Formula III, while including, for example,a branching unit B with higher branching, or including an X₁ moietyfeaturing two (meth)acrylate moieties as defined herein, or similar tothose presented in Formula II, while including, for example, another(meth)acrylate moiety that is attached to the elastomeric moiety.

In some embodiments, the elastomeric moiety, e.g., Re in Formula I orthe moiety denoted as E in Formulae I*, II and III, is or comprises analkyl, which can be linear or branched, and which is preferably of 3 ormore or of 4 or more carbon atoms; an alkylene chain, preferably of 3 ormore or of 4 or more carbon atoms in length; an alkylene glycol asdefined herein, an oligo(alkylene glycol), or a poly(alkylene glycol),as defined herein, preferably of 4 or more atoms in length, a urethane,an oligourethane, or a polyurethane, as defined herein, preferably of 4or more carbon atoms in length, and any combination of the foregoing.

In some of any of the embodiments described herein, the elastomericcurable material is a (meth)acrylic curable material, as describedherein, and in some embodiments, it is an acrylate.

In some of any of the embodiments described herein, the elastomericcurable material is or comprises a mono-functional elastomeric curablematerial, and is some embodiments, the mono-functional elastomericcurable material is represented by Formula I, wherein R₁ is —C(═O)—ORaand Ra is an alkylene chain (e.g., of 4 or more, preferably 6 or more,preferably 8 or more, carbon atoms in length), or a poly(alkyleneglycol) chain, as defined herein.

In some embodiments, the elastomeric curable material is or comprises amulti-functional elastomeric curable material, and is some embodiments,the multi-functional elastomeric curable material is represented byFormula I*, wherein E is an alkylene chain (e.g., of 4 or more, or 6 ormore, carbon atoms in length), and/or a poly(alkylene glycol) chain, asdefined herein.

In some embodiments, the elastomeric curable material is or comprises amulti-functional elastomeric curable material, and is some embodiments,the multi-functional elastomeric curable material is represented byFormula II, wherein E is a branched alkyl (e.g., of 3 or more, or of 4or more, or of 5 or more, carbon atoms in length).

In some of any of the embodiments described herein, the elastomericcurable material is an elastomeric acrylate or methacrylate (alsoreferred to as acrylic or methacrylic elastomer), for example, ofFormula I, I*, II or III, and in some embodiments, the acrylate ormethacrylate is selected such that when hardened, the polymeric materialfeatures a Tg lower than 0° C. or lower than −10° C.

Exemplary elastomeric acrylate and methacrylate curable materialsinclude, but are not limited to, 2-propenoic acid,2-[[(butylamino)carbonyl]oxy]ethyl ester (an exemplary urethaneacrylate), and compounds marketed under the trade names SR335 (Laurylacrylate) and SR395 (isodecyl acrylate) (by Sartomer). Other examplesinclude compounds marketed under the trade names SR350D (a trifunctionaltrimethylolpropane trimethacrylate (TMPTMA), SR256(2-(2-ethoxyethoxy)ethyl acrylate, SR252 (polyethylene glycol (600)dimethacrylate), SR561 (an alkoxylated hexane diol diacrylate) (bySartomer).

It is to be notes that other acrylic materials, featuring, for example,one or more acrylamide groups instead of one or more acrylate ormethacrylate groups are also contemplated.

In some of any of the embodiments described herein, the elastomericcurable material comprises one or more mono-functional elastomericcurable material(s) (e.g., a mono-functional elastomeric acrylate, asrepresented, for example, in Formula I) and one or more multi-functional(e.g., di-functional) elastomeric curable materials(s) (e.g., adi-functional elastomeric acrylate, as represented, for example, inFormula I*, II or III) and in any of the respective embodiments asdescribed herein.

In some of any of the embodiments described herein, a total amount ofthe elastomeric curable material(s) is at least 40%, or at last 50%, orat least 60%, and can be up to 70% or even 80%, of the total weight ofan elastomeric modeling material formulation as described herein.

In some of any of the embodiments described herein, the elastomericcurable modeling formulation further comprises silica particles.

In some of any of the embodiments described herein, the silica particleshave an average particle size lower than 1 micron, namely, the silicaparticles are sub-micron particles. In some embodiments, the silicaparticles are nano-sized particles, or nanoparticles, having an averageparticle size in the range of from 0.1 nm to 900 nm, or from 0.1 nm to700 nm, or from 1 nm to 700 nm, or from 1 nm to 500 nm or from 1 nm to200 nm, including any intermediate value and subranges therebetween.

In some embodiments, at least a portion of such particles may aggregate,upon being introduced to the formulation. In some of these embodiments,the aggregate has an average size of no more than 3 microns, or no morethan 1.5 micron.

Any commercially available formulations of sub-micron silica particlesis usable in the context of the present embodiments, including fumedsilica, colloidal silica, precipitated silica, layered silica (e.g.,montmorillonite), and aerosol assisted self-assembly of silicaparticles.

The silica particles can be such that feature a hydrophobic orhydrophilic surface. The hydrophobic or hydrophilic nature of theparticles' surface is determined by the nature of the surface groups onthe particles.

When the silica is untreated, namely, is composed substantially of Siand O atoms, the particles typically feature silanol (Si—OH) surfacegroups and are therefore hydrophilic. Untreated (or uncoated) colloidalsilica, fumed silica, precipitated silica and layered silica all featurea hydrophilic surface, and are considered hydrophilic silica.

Layered silica may be treated so as to feature long-chain hydrocarbonsterminating by quaternary ammonium and/or ammonium as surface groups,and the nature of its surface is determined by the length of thehydrocarbon chains. Hydrophobic silica is a form of silica in whichhydrophobic groups are bonded to the particles' surface, and is alsoreferred to as treated silica or functionalized silica (silica reactedwith hydrophobic groups).

Silica particles featuring hydrophobic surface groups such as, but notlimited to, alkyls, preferably medium to high alkyls of 2 or more carbonatoms in length, preferably of 4 or more, or 6 or more, carbon atoms inlength, cycloalkyls, aryl, and other hydrocarbons, as defined herein, orhydrophobic polymers (e.g., polydimethylsiloxane), are particles ofhydrophobic silica.

Silica particles as described herein can therefore by untreated(non-functionalized) and as such are hydrophilic particles.

Alternatively, silica particles as described herein can be treated, orfunctionalized, by being reacted so as to form bonds with the moietieson their surface.

When the moieties are hydrophilic moieties, the functionalized silicaparticles are hydrophilic.

Silica particles featuring hydrophilic surface groups such as, but notlimited to, hydroxy, amine, ammonium, carboxy, silanol, oxo, and thelike, are particles of hydrophilic silica.

When the moieties are hydrophobic moieties, as described herein, thefunctionalized silica particles are hydrophobic.

In some of any of the embodiments described herein, at least a portion,or all, of the silica particles feature a hydrophilic surface (namely,are hydrophilic silica particles, for example, of untreated silica suchas colloidal silica).

In some of any of the embodiments described herein, at least a portion,or all, of the silica particles feature a hydrophobic surface (namely,are hydrophobic silica particles).

In some embodiments, the hydrophobic silica particles are functionalizedsilica particles, namely, particles of silica treated with one or morehydrophobic moieties.

In some of any of the embodiments described herein, at least a portion,or all, of the silica particles are hydrophobic silica particles,functionalized by curable functional groups (particles featuring curablegroups on their surface).

The curable functional groups can be any polymerizable group asdescribed herein. In some embodiments, the curable functional groups arepolymerizable by the same polymerization reaction as the curablemonomers in the formulation, and/or when exposed to the same curingcondition as the curable monomers. In some embodiments, the curablegroups are (meth)acrylic (acrylic or methacrylic) groups, as definedherein.

Hydrophilic and hydrophobic, functionalized and untreated silicaparticles as described herein can be commercially available materials orcan be prepared using methods well known in the art.

By “at least a portion”, as used in the context of these embodiments, itis meant at least 10%, or at least 20%, or at least 30%, or at least40%, or at least 50%, or at least 60%, or at least 70%, or at least 80%,or at least 90%, or at least 95%, or at least 98%, of the particles.

The silica particles may also be a mixture of two or more types ofsilica particles, for example, two or more types of any of the silicaparticles described herein.

In some of any of the embodiments described herein, an amount of thesilica particles in a modeling material formulation comprising sameranges from about 1% to about 20%, or from about 1% to about 15%, orfrom about 1% to about 10%, by weight, of the total weight of themodeling material formulation.

In some of any of the embodiments described herein, an amount of thesilica particles in a formulation system as described herein ranges fromabout 1% to about 20%, or from about 1% to about 15%, or from about 1%to about 10%, by weight, of the total weight of the formulation system.

In some embodiments, the formulation system comprises one formulation.In some embodiments, the formulation system comprises two or moreformulations, and the silica particles are comprised within 1, 2 or allthe formulations.

The amount of the silica particles can be manipulated as desired so asto control the mechanical properties of the cured modeling materialand/or the object or part therein comprising same. For example, higheramount of silica particles may result in higher elastic modulus of thecured modeling material and/or the object or part thereof comprisingsame.

In some of any of the embodiments described herein, an amount of thesilica particles is such that a weight ratio of the elastomeric curablematerial(s) and the silica particles in the one or more modelingmaterial formulation(s) ranges from about 50:1 to about 4:1 or fromabout 30:1 to about 4:1 or from about 20:1 to about 2:1, including anyintermediate values and subranges therebetween.

According to some of any of the embodiments described herein, theelastomeric modeling material formulation further comprises one or moreadditional curable material(s).

The additional curable material can be a mono-functional curablematerial, a multi-functional curable material, or a mixture thereof, andeach material can be a monomer, an oligomer or a polymer, or acombination thereof.

Preferably, but not obligatory, the additional curable material ispolymerizable when exposed to the same curing energy at which thecurable elastomeric material is polymerizable, for example, uponexposure to irradiation (e.g., UV-vis irradiation).

In some embodiments, the additional curable material is such that whenhardened, the polymerized material features Tg higher than that of anelastomeric material, for example, a Tg higher than 0° C., or higherthan 5° C. or higher than 10° C.

In some embodiments, the additional curable material is anon-elastomeric curable material, featuring, for example, when hardened,Tg and/or Elastic Modulus that are different from those representingelastomeric materials.

In some embodiments, the additional curable material is amono-functional acrylate or methacrylate ((meth)acrylate). Non-limitingexamples include isobornyl acrylate (IBOA), isobornylmethacrylate,acryloyl morpholine (ACMO), phenoxyethyl acrylate, marketed by SartomerCompany (USA) under the trade name SR-339, urethane acrylate oligomersuch as marketed under the name CN 131B, and any other acrylates andmethacrylates usable in AM methodologies.

In some embodiments, the additional curable material is amulti-functional acrylate or methacrylate ((meth)acrylate). Non-limitingexamples of multi-functional (meth)acrylates include propoxylated (2)neopentyl glycol diacrylate, marketed by Sartomer Company (USA) underthe trade name SR-9003, Ditrimethylolpropane Tetra-acrylate (DiTMPTTA),Pentaerythitol Tetra-acrylate (TETTA), and DipentaerythitolPenta-acrylate (DiPEP), and an aliphatic urethane diacrylate, forexample, such as marketed as Ebecryl 230. Non-limiting examples ofmulti-functional (meth)acrylate oligomers include ethoxylated ormethoxylated polyethylene glycol diacrylate or dimethacrylate,ethoxylated bisphenol A diacrylate, polyethylene glycol-polyethyleneglycol urethane diacrylate, a partially acrylated polyol oligomer,polyester-based urethane diacrylates such as marketed as CNN91.

Any other curable materials, preferably curable materials featuring a Tgas defined herein, are contemplated as an additional curable material.

In some of any of the embodiments described herein, the elastomericmodeling material formulation further comprises an initiator, forinitiating polymerization of the curable materials.

When all curable materials (elastomeric and additional, if present) arephotopolymerizable, a photoinitiator is usable in these embodiments.

When all curable materials (elastomeric and additional, if present) areacrylic compounds or otherwise are photopolymerizable by free radicalpolymerization, a free radical photoinitiator, as described herein, isusable in these embodiments.

A concentration of a photoinitiator in a curable elastomeric formulationcontaining same may range from about 0.1 to about 5 weight percents, orfrom about 1 to about 5 weight percents, including any intermediatevalue and subranges therebetween.

According to some of any of the embodiments described herein, theelastomeric modeling material formulation further comprises one or moreadditional, non-curable material(s), for example, one or more of acolorant, a dispersant, a surfactant, a stabilizer and an inhibitor, asdescribed herein for a soft modeling material formulation.

In some of any of the embodiments described herein, the elastomericcurable material is a UV curable material, and in some embodiments, itis an elastomeric (meth)acrylate, for example, an elastomeric acrylate.

In some of any of the embodiments described herein, an additionalcurable component is included in the elastomeric modeling materialformulation, and in some embodiments, this component is a UV-curableacrylate or methacrylate.

In some of any of the embodiments described herein, the silica particlesare (meth)acrylate-functionalized silica particles.

In some of any of the embodiments described herein, the elastomericmodeling material formulation comprises one or more mono-functionalelastomeric acrylate, one or more multi-functional elastomeric acrylate,one or more mono-functional acrylate or methacrylate and one or moremulti-functional acrylate or methacrylate.

In some of these embodiments, the elastomeric modeling materialformulation further comprises one or more photoinitiators, for example,of the Irgacure® family.

In some of any of the embodiments described herein, all the curablematerials and the silica particles the elastomeric modeling formulationare included in a single material formulation.

In some of any of the embodiments described herein, the elastomericmodeling formulation comprises two or more modeling materialformulations and forms an elastomeric formulation system comprising anelastomeric curable formulation as described herein.

In some of these embodiments, one modeling material formulation (e.g., afirst formulation, or Part A) comprises an elastomeric curable material(e.g., an elastomeric acrylate) and another modeling materialformulation (e.g., a second formulation, or Part B) comprises anadditional curable material.

Alternatively, each of the two modeling material formulations comprisesan elastomeric curable material and one of the formulations furthercomprises an additional curable material.

Further alternatively, each of the two modeling material formulations inthe elastomeric formulation system comprises an elastomeric curablematerial, yet, the elastomeric materials are different in eachformulation. For example, one formulation comprises a mono-functionalelastomeric curable material and another formulation comprises amulti-functional elastomeric material. Alternatively, one formulationcomprises a mixture of mono-functional and multi-functional elastomericcurable materials at a ratio W and another formulation comprises amixture of mono-functional and multi-functional elastomeric curablematerials at a ratio Q, wherein W and Q are different.

Whenever each of the modeling material formulations comprises anelastomeric material as described herein, one or more of the modelingmaterial formulations in the elastomeric formulation system can furthercomprise an additional curable material. In exemplary embodiments, oneof the formulations comprises a mono-functional additional material andanother comprises a multi-functional additional material. In furtherexemplary embodiments, one of the formulations comprises an oligomericcurable material and another formulation comprises a monomeric curablematerial.

Any combination of elastomeric and additional curable materials asdescribed herein is contemplated for inclusion in the two or moremodeling material formulations forming the elastomeric formulationsystem. Selecting the composition of the modeling material formulationsand the printing mode allows fabrication of objects featuring a varietyof properties in a controllable manner, as is described in furtherdetail hereinbelow.

In some embodiments, the one or more modeling material formulations inan elastomeric formulation system are selected such that a ratio of anelastomeric curable material and an additional curable material providesa rubbery-like material as described herein.

In some embodiments, silica particles, one or more photoinitiators, andoptionally other components, are included in one or both modelingmaterial formulations.

In exemplary modeling material formulations according to some of any ofthe embodiments described herein, all curable materials are(meth)acrylates.

In any of the exemplary modeling material formulations described herein,a concentration of a photoinitiator ranges from about 1% to about 5% byweight, or from about 2% to about 5%, or from about 3% to about 5%, orfrom about 3% to about 4% (e.g., 3, 3.1, 3.2, 3.25, 3.3, 3.4, 3.5, 3.6,3.7, 3.8, 3.85, 3.9, including any intermediate value therebetween) %,by weight, of the total weight of the formulation or formulation systemcomprising same.

In any of the exemplary modeling material formulations described herein,a concentration of an inhibitor ranges from 0 to about 2% weight, orfrom 0 to about 1%, and is, for example, 0, 0.1, 0.2, 0.3, 0.4, 0.5,0.6, 0.7, 0.8, 0.9 or about 1%, by weight, including any intermediatevalue therebetween, of the total weight of the formulation or aformulation system comprising same.

In any of the exemplary modeling material formulations described herein,a concentration of a surfactant ranges from 0 to about 1% weight, andis, for example, 0, 0.01, 0.05, 0.1, 0.5 or about 1%, by weight,including any intermediate value therebetween, of the total weight ofthe formulation or formulation system comprising same.

In any of the exemplary modeling material formulations described herein,a concentration of a dispersant ranges from 0 to about 2% weight, andis, for example, 0, 0.1, 0.5, 0.7, 1, 1.2, 1.3, 1.35, 1.4, 1.5, 1.7, 1.8or about 2%, by weight, including any intermediate value therebetween,of the total weight of the formulation or formulation system comprisingsame.

In exemplary modeling material formulations according to some of any ofthe embodiments described herein, a total concentration of anelastomeric curable material ranges from about 30% to about 90% byweight, or from about 40% to about 90%, by weight, or from about 40% toabout 85%, by weight.

By “total concentration” it is meant herein throughout a total weight inall of the (one or more) elastomeric modeling material formulations, orin an elastomeric formulation system as described herein.

In some embodiments, the elastomeric curable material comprises amono-functional elastomeric curable material and a multi-functionalelastomeric curable material.

In some embodiments, a total concentration of the mono-functionalelastomeric curable material ranges from about 20% to about 70%, or fromabout 30% to about 50%, by weight, including any intermediate value andsubranges therebetween. In exemplary embodiments, a total concentrationof the mono-functional elastomeric curable material ranges from about50% to about 70%, or from about 55% to about 65%, or from about 55% toabout 60% (e.g. 58%), by weight, including any intermediate value andsubranges therebetween. In exemplary embodiments, a total concentrationof the mono-functional elastomeric curable material ranges from about30% to about 50%, or from about 35% to about 50%, or from about 40% toabout 45% (e.g., 42%), by weight, including any intermediate value andsubranges therebetween.

In some embodiments, a total concentration of the multi-functionalelastomeric curable material ranges from about 10% to about 30%, byweight. In exemplary embodiments, a concentration of the mono-functionalelastomeric curable material ranges from about 10% to about 20%, or fromabout 10% to about 15% (e.g. 12%), by weight. In exemplary embodiments,a concentration of the mono-functional elastomeric curable materialranges from about 10% to about 30%, or from about 10% to about 20%, orfrom about 15% to about 20% (e.g., 16%), by weight.

In exemplary modeling material formulations according to some of any ofthe embodiments described herein, a total concentration of an additionalcurable material ranges from about 10% to about 40% by weight, or fromabout 15% to about 35%, by weight, including any intermediate value andsubranges therebetween.

In some embodiments, the additional curable material comprises amono-functional curable material.

In some embodiments, a total concentration of the mono-functionaladditional curable material ranges from about 15% to about 25%, or fromabout 20% to about 25% (e.g., 21%), by weight, including anyintermediate value and subranges therebetween. In exemplary embodiments,a concentration of the mono-functional elastomeric curable materialranges from about 20% to about 30%, or from about 25% to about 30%(e.g., 28%), by weight, including any intermediate value and subrangestherebetween.

In exemplary elastomeric modeling material formulations or formulationsystems comprising same according to some of any of the embodimentsdescribed herein, the elastomeric curable material comprises amono-functional elastomeric curable material and a multi-functionalelastomeric curable material; a total concentration of themono-functional elastomeric curable material ranges from about 30% toabout 50% (e.g., from about 40% to about 45%) or from about 50% to about70% (e.g., from about 55% to about 60%) by weight; and a totalconcentration of the multi-functional elastomeric curable materialranges from about 10% to about 20% by weight; and the one or moreformulation(s) further comprise(s) an additional mono-functional curablematerial at a total concentration that ranges from about 20% to about30%, by weight.

According to some of any of the embodiments described herein, the one ormore modeling formulation(s) comprise(s) at least one elastomericmono-functional curable material, at least one elastomericmulti-functional curable material and at least additionalmono-functional curable material.

According to some of any of the embodiments described herein, a totalconcentration of the curable mono-functional material ranges from 10% to30%, by weight of the total weight of the one or more modelingformulation(s).

According to some of any of the embodiments described herein, a totalconcentration of the elastomeric mono-functional curable material rangesfrom 50% to 70%, by weight, of the total weight of the one or moremodeling formulation(s).

According to some of any of the embodiments described herein, a totalconcentration of the elastomeric multi-functional curable materialranges from 10% to 20%, by weight, of the total weight of the one ormore modeling formulation(s).

According to some of any of the embodiments described herein, a totalconcentration of the curable mono-functional material ranges from 10% to30%, by weight; a total concentration of the elastomeric mono-functionalcurable material ranges from 50% to 70%, by weight; and a totalconcentration of the elastomeric multi-functional curable materialranges from 10% to 20%, by weight, of the total weight of the one ormore modeling formulation(s).

According to some of any of the embodiments described herein, a totalconcentration of the curable mono-functional material ranges from 20% to30%, by weight, of the total weight of the one or more modelingformulation(s).

According to some of any of the embodiments described herein, a totalconcentration of the elastomeric mono-functional curable material rangesfrom 30% to 50%, by weight, of the total weight of the one or moremodeling formulation(s).

According to some of any of the embodiments described herein, a totalconcentration of the elastomeric multi-functional curable materialranges from 10% to 30%, by weight, of the total weight of the one ormore modeling formulation(s).

According to some of any of the embodiments described herein, a totalconcentration of the curable mono-functional material ranges from 20% to30%, by weight; a total concentration of the elastomeric mono-functionalcurable material ranges from 30% to 50%, by weight; and a totalconcentration of the elastomeric multi-functional curable materialranges from 10% to 30%, by weight, of the total weight of the one ormore modeling formulation.

In the exemplary modeling material formulations described herein, aconcentration of each component is provided as its concentration whenone modeling material formulations is used or as its total concentrationin two or more modeling material formulations.

In some embodiments, an elastomeric modeling material formulation (orthe two or more modeling material formulations) as described herein, ischaracterized, when hardened, by Tear Resistance of at least 4,000 N/m,or at least 4500 N/m or at least 5,000 N/m, whereby the Tear Resistanceis determined according to ASTM D 624.

In some embodiments, an elastomeric modeling material formulation (orthe two or more modeling material formulations) as described herein, ischaracterized, when hardened, by Tear Resistance higher by at least 500N/m, or by at least 700 N/m, or by at least 800 N/m, than that of thesame modeling material formulation(s) devoid of said silica particles,when hardened.

In some embodiments, an elastomeric modeling material formulation (orthe two or more modeling material formulations) as described herein, ischaracterized, when hardened, by Tensile Strength of at least 2 MPa.

In some embodiments, an elastomeric modeling material formulation (orthe two or more modeling material formulations) as described herein, issuch that an object consisting of the cured modeling material andfeaturing two O-rings and a tube connecting the rings, is characterizedby Tear Resistance under constant elongation of at least one hour, or atleast one day.

According to some of any of the embodiments described herein, theelastomeric curable material is selected from a mono-functionalelastomeric curable monomer, a mono-functional elastomeric curableoligomer, a multi-functional elastomeric curable monomer, amulti-functional elastomeric curable oligomer, and any combinationthereof, as described herein for an elastomeric curable material in anyof the respective embodiments and any combination thereof.

In some embodiments, the elastomeric curable material comprises one ormore materials selected from the materials represented by Formula I, I*,II and III, as described herein in any of the respective embodiments andany combination thereof.

According to some of any of the embodiments described herein, theelastomeric curable material and the silica particles are in the sameformulation.

According to some of any of the embodiments described herein, theelastomeric curable formulation system further comprises at least oneadditional curable material.

According to some of any of the embodiments described herein, theadditional curable material is selected from a mono-functional curablemonomer, a mono-functional curable oligomer, a multi-functional curablemonomer, a multi-functional curable oligomer and any combinationthereof, as described herein for an additional curable material in anyof the respective embodiments and any combination thereof.

According to some of any of the embodiments described herein, theelastomeric curable material, the silica particles and the additionalcurable material are in the same formulation.

According to some of any of the embodiments described herein, theelastomeric curable material is a UV-curable elastomeric material.

According to some of any of the embodiments described herein, theelastomeric curable material is an acrylic elastomer.

Example 4 Distance Field and Modulation Functions

The present example describes a method that includes selecting a voxelfrom a three-dimensional build space and for the selected voxel,determining a distance field value relative to a three-dimensional partin the three-dimensional build space. The method can be used forpreparing computer object data for use in systems 110 and 10 accordingto some embodiments of the present invention. At least some of thedescription below is also described in international patent applicationNo. PCT/US2017/019340, filed on Feb. 24, 2017, the contents of which arehereby incorporated by reference.

The distance field value can be used to select at least one materialselection rule and a feature of the voxel is applied to the at least onematerial selection rule to identify a material designation for thevoxel. The material designation indicates no material is to be placed atthe voxel when the material selection rule identifies no material forthe voxel and the material designation indicates at least one materialis to be placed at the voxel when the at least one material selectionrule identifies the at least one material for the voxel. The materialdesignation for the voxel is then output for use in building thethree-dimensional part using an additive manufacturing system.

In some embodiments of the present invention the method includesselecting a voxel in a three-dimensional build space, determining afirst distance field value for the voxel relative to a boundary of afirst three-dimensional part positioned in the three-dimensional buildspace, and determining a second distance field value for the voxelrelative to a boundary of a second three-dimensional part positioned inthe three-dimensional build space. The first distance field value andthe second distance field value are then used to set a materialdesignation for the voxel.

To build a part using additive manufacturing, instructions must beprovided to the printer to indicate what material, if any, should beplaced in each of the available locations of each printing layer. In thepast, these instructions were produced by identifying the exteriorbounds of each part at each slice using boundary representations. A partmaterial was then designated for each location that was positioned alongthe boundary of the part. If the part was to be solid, the material setfor the part was also designated for each location within the boundariesof the part. In such systems, all material transitions, either from onematerial to another material, or from a material to open space, had tobe described by a boundary representation.

The present inventors have discovered that relying on such boundaryrepresentations to control transitions between materials creates severalproblems. First, performing rounding, lofting and offset modelingoperations where boundary representations are shifted inward or outwardto produce the print instructions can produce errors or unexpectedresults due to interference between shifted boundary representations.This typically occurs when the topology of the part is complex. Second,Boolean operations, such as subtraction or union, which are performedbetween two different parts when generating print instructions, can failif the boundary representations of the parts do not define an enclosedobject. Any opening in the part will cause the Boolean operations to belimited to the boundary representation itself instead of the completevolume of the part. Third, it is extremely difficult to define latticesusing boundary representations because the lattices require a hugenumber of meshes resulting in a large amount of data. Fourth, it is notpossible to form material gradients in which a mixture of materialschanges over some dimension of the part.

In the embodiments described below, the problems associated withboundary representations are overcome by using distance fields. In oneembodiment, a distance field is created by dividing thethree-dimensional build space, which contains the part(s) to bemanufactured, into a three-dimensional matrix of voxels. The closestdistance from each voxel to a part boundary is then determined such thatif the voxel is within the part, the distance is set as a positivevalue, if the voxel is outside of the part, the distance is set as anegative value and if the voxel is on the part boundary, the distance iszero. This produces a three-dimensional matrix of distance field values.Each part has its own associated distance field. As a result, when thereare multiple parts in the build space, each voxel has multiple differentdistance field values, each associated with a separated part.

Once the distance fields are determined, they are used to select atleast one material selection rule for each voxel. Each materialselection rule identifies a material designation for the voxel using atleast one feature of the voxel such as the distance field value of thevoxel and the position of the voxel in the build space, for example. Insome embodiments, the material selection rule includes a periodicfunction that is a function of the distance field values and/or theposition in the build space such that one range of output valuesproduced by the periodic function is associated with no material beingdesignated for the voxel and another range of output values produced bythe periodic function is associated with a material being designated forthe voxel. Such periodic functions allow lattices to be defined in thebuild space.

FIG. 9 shows an example of a simplified system for assigning materialsto voxels and manufacturing parts using the assigned materials. In FIG.9 , a computer 9066 acts as a host computer for an additivemanufacturing system 9068 and communicates with system 9068 over one ormore communication lines 9070. In some embodiments, computer 9066 isinternal to system 9068, such as part of an internal controller assemblyfor system 9068. In other embodiments, computer 9066 is external toadditive manufacturing system 9068.

FIG. 10 shows a block diagram of an example architecture for computer9066. As shown, computer 9066 includes suitable computer-based hardware,such as a user interface 9082, a memory controller 9084, a processor9086, a graphics processing unit 9087, a storage media 9088, aninput/output (I/O) controller 9090, and a communication adapter 9092.Computer 9066 may also include a variety of additional components thatare contained in conventional computers, servers, media devices, signalprocessing devices, and/or printer controllers.

User interface 9082 is one or more user-operated interfaces (e.g.,keyboards, touch pads, touch-screen displays, display monitors, andother eye, voice, movement, or hand-operated controls) configured tooperate computer 9066. Memory controller 9084 is one or more circuitassemblies that interface the components of computer 9066 with one ormore volatile random access memory (RAM) modules of storage media 9088.Processor 9086 is one or more computer-processing units configured tooperate computer 9066, optionally with memory controller 9084, andpreferably with related processing circuitry (e.g., programmable gatearrays, digital and analog components, and the like). For instance,processor 9086 may include one or more microprocessor-based and/ormicrocontroller-based units, one or more central processing units,and/or one or more front-end processing units.

Graphics processing unit 9087 contains a large number of transistorsthat are arranged to perform calculations related to 3D computergraphics in a fast an efficient manner. Such calculations includetexture mapping and rendering polygons that represent 3D objects.

Storage media 9088 is one or more internal and/or external data storagedevices or computer storage media for computer 9066, such as volatileRAM modules, read-only memory modules, optical media, magnetic media(e.g., hard disc drives), solid-state media (e.g., FLASH memory andsolid-state drives), analog media, and the like. Storage media 9088 mayretain one or more pre-processing and/or post-processing programs (notshown) discussed further below.

I/O controller 9090 is one or more circuit assemblies that interfacememory controller 9084, processor 9086, and storage media 9088 withvarious input and output components of computer 9066, including userinterface 9082 and communication adapter 9092. Communication adapter9092 is one or more wired and/or wireless transmitter/receiver adaptersconfigured to communicate over communication lines 9070.

The commands from computer 9066 to the components of systems 9068 may beperformed with one or more of user interface 9082, memory controller9084, processor 9086, storage media 9088, input/output (I/O) controller9090, communication adapter 9092, and/or other suitable hardware andsoftware implementations, as is understood by those skilled in the art.

FIG. 11 provides a flow diagram of a method of generating printinstructions from part models using distance fields. FIG. 12 provides ablock diagram of a system 9200 used to implement the method of FIG. 11 .In accordance with one embodiment, system 9200 is implemented incomputer 9066.

In step 9100, part data is received including meshes 9202, texture maps9204, bump maps 9206, shine maps 9208, point features 9209 and a partresolution, which are stored in storage media 9088. Meshes 9202 describeplanar boundaries of the part and can be defined as interconnectedtriangles or interconnected quadrilaterals. Texture maps 9204 describethe location and geometry of surface textures to be applied on theoutside of each of the surfaces described by meshes 9202. Bump maps 9206provide descriptions of larger surface features present on particularsurfaces of the meshes 9202. FIG. 13 provides an example of a portion ofa part showing two surfaces 9300 and 9302 having textures marked by theraised squares 9304 and a surface bump 9306 represented by the largeraised square. The small squares 9304 would be described in the texturemaps 9204 while the surface bump 9306 would be described in the bumpmaps 9206. Shininess maps 9208 indicate a desired level of shine fordifferent surfaces of the part.

Point features 9209 describe sets of material selection rules to be usedfor portions of the part having specific features. Examples of partfeatures that can be used as the basis for assigning sets of materialselection rules include identifiers of a body or mesh, surface texturecoordinates, and surface normal ranges. Thus, in some embodiments,different portions of a part have different sets of material selectionrules such that at the same distance field values, different materialswill be used for different areas around the part. A further descriptionof the use of such point features is provided below.

Meshes 9202, texture maps 9204 and bump maps 9206 are provided to aslice computations process 9210 executed by graphics processing unit9087, which performs step 9101-9116, 9120, 9122 and 9124 of FIG. 11described further below.

At step 9101, slice computations process 9210 defines athree-dimensional build space and orients the parts described by meshes9202, texture maps 9204 and bump maps 9206 in the three-dimensionalbuild space to form oriented digital models 9091. In accordance with oneembodiment, the build space is defined by first orienting the digitalparts and then defining a bounding box around the oriented parts toprovide a support structure envelope around the parts.

FIG. 14 provides a three-dimensional view of a three-dimensional partmodel 402 oriented in a three-dimensional build space 400. In FIG. 14 ,there is a −Z direction 406, a +Z direction 408, an X direction 410 anda Y direction 412. A slice 400 of build space 400 is shown to include acollection of voxels, such as voxel 414. Although only a single slice isshown in FIG. 14 , there are multiple slices in build space 400 suchthat voxels fill the entirety of build space 400. The dimensions of thevoxels are based on the resolution set for the part.

At step 9102, slice computations process 9210 sets values for Z buffer9095 for each slice in build space 400. The Z buffer for a slicecontains a value for each voxel in the slice, where the magnitude of theZ buffer value represents the magnitude of the vertical distance betweenthe voxel and the closest STL boundary of the part. The STL boundary ofthe part is constructed from the combination of one or more meshes 9202,texture maps 9204 applied to those meshes, and bump maps 9206 applied tothose meshes. In step 9102, this distance is determined by looking in −Zdirection 406 from the voxel and the Z buffer is therefore referred toas the −Z buffer. The sign of the Z buffer value indicates whether thevoxel is inside or outside the part with negative values indicating thatthe voxel is outside of the part and positive values indicating that thevoxel is inside the part. Initially, all of the −Z buffer values for aslice are set to a maximum negative value, which indicates that noportion of the part is visible in −Z direction 406 from any of voxels.

A rendering operation is then performed by GPU90 87 using meshes 9202,texture maps 9204 and bump maps 9206 to construct a description of theSTL boundaries of the part in three-dimensional build space 400 and toproject that description onto the slice. In particular, each surface inmeshes 9202 are rendered one at a time and the texture maps 9204 andbump maps 9206 are applied to the rendered surfaces to produce the STLboundaries for the surface and the resulting STL boundaries for thesurfaces are projected onto the slice by identifying the voxels that aredirectly above the STL boundaries in the three-dimensional build space.For each voxel that is directly above the STL boundaries of a surface,the distance between the STL boundary and the voxel is compared to thecurrent distance stored in the −Z buffer for the voxel. If the distanceto the surface currently being projected has a smaller magnitude thanthe value stored in the −Z buffer, the current surface is considered tobe closer to the voxel than any previously rendered surfaces of the partand the −Z buffer is updated with the distance to the current STLboundary. The sign of the distance value stored in the −Z buffer is setto indicate whether the voxel is inside or outside the part. This can bedetermined based on the angle between the outward normal of the currentsurface and the +Z direction 408. In accordance with one embodiment, theidentity of the current surface is also stored in an additional bufferfor the slice. If the distance between the current STL boundary and thevoxel is larger than the magnitude of the Z buffer value for the voxel,the Z buffer value remains unchanged. This will occur when the currentsurface is obscured from the voxel by another surface of the part, whichis closer to the voxel. Thus, after every surface of the part below thecurrent slice has been rendered and projected onto the slice, the Zbuffer contains values indicating the shortest distance in the Zdirection between the voxel and the STL boundary of the part and afurther buffer indicates the identity of those closest surfaces. This isrepeated for each slice in build space 400.

The loading of Z buffers using graphical processing units is common inrendering 3D computer models of objects onto 2D planes. However, usingsuch graphical processing units to load Z buffers associated with voxelsas part of constructing three-dimensional parts has not been known.

After the −Z buffers have been formed for all of the slices in buildspace 400 the lowest slice in build space 400 is selected at step 9104.At step 9106, a rendering operation is performed in the +Z direction toload a +Z buffer for the selected slice. This rendering is identical tothe rendering performed in the −Z direction with the exception that theview is changed to +Z direction 408. After step 9106, the selected slicehas a +Z buffer value for each voxel and a −Z buffer value for eachvoxel where the +Z buffer value provides the shortest vertical distancebetween the voxel and the part in +Z direction 408 and the −Z buffervalue provides the shortest distance between the voxel and the part in−Z direction 406.

Although steps 9102 and 9106 are described above with reference to onepart in build space 400, in other embodiments, multiple parts arepresent in build space 400. When multiple parts are present in buildspace 400, a separate −Z buffer and a separate +Z buffer is created foreach part for each slice in build space 400.

At step 9108, silhouette boundaries for the selected slice aredetermined from the +Z buffer(s). In particular, the +Z buffer valuesfor pairs of voxels are examined to identify transitions from a negativevalue to the greatest magnitude negative value possible. Suchtransitions represent a boundary between where a portion of a part isabove a voxel and no portion of the part is above the voxel's neighbor.An example of such a boundary can be seen in FIG. 14 where voxels 420and 422 are positioned along such a boundary. Voxel 420 is positionedbelow part 402 and has a +Z buffer value of −4. Voxel 422, whichneighbors voxel 420, is not below any portion of the part and as suchhas the largest possible negative value, for example −10000, in the+Z-buffer. Repeating this pairwise comparison for every pair producessilhouette boundaries, such as silhouette boundary 424 where voxelswithin the boundary are considered to be underneath a portion of thepart and voxels outside of the silhouette are not below any portions ofa part. Note that when multiple parts are present in build space 400,step 9108 is repeated for each +Z buffer for the slice selected at step9104.

At step 9110, slice computations process 9210 determines theintersections of STL boundaries with the current slice. In FIG. 14 , theintersection of the STL boundary and slice 400 is shown as boundary 430,shown in dotted lines. The intersection of the STL boundaries with theslice can be found by examining the +Z buffer and the −Z buffer toidentify neighboring pixels where the Z buffer value changes from anegative value to a value of 0 or from a negative value to a positivevalue. Such changes in the Z-buffer values indicate a transition frombeing outside of the part to being within the part. Step 9110 isperformed for each part's Z buffers.

At step 9112, a single voxel in the current slice is selected. At step9114, a distance field value to the part's STL boundaries is determinedfor the voxel. This distance field value is the shortest magnitudedistance between the voxel and any portion of the part's STL boundaries.At step 9116, if the current voxel is outside of the part, the distanceto the silhouette boundary is determined for the current voxel.

In accordance with one embodiment, steps 9114 and 9116 are performedtogether using a sampling algorithm. One example of such a samplingalgorithm is shown in the flow diagram of FIG. 15 , which is explainedwith reference to FIG. 16 . In FIG. 16 , a top view of a slice 620 isshown with a matrix of voxels, including current voxel 600. An STLboundary 612 that intersects slice 600 is shown as a solid line and asilhouette boundary 610 is shown as a dotted line.

At step 500 of FIG. 15 , the current voxel, voxel 600 of FIG. 16 , isexamined to determine if it is at an STL boundary in the current slice.For example, in FIG. 16 , voxel 650 would be considered to be at STLboundary 612 since STL boundary 612 intersects with voxel 650. If thecurrent voxel is at the STL boundary at step 500, the distance fieldvalue is set to 0 for the current voxel at step 502.

If the current voxel is not at the STL boundary at step 500, as is shownwith current voxel 600 of FIG. 16 , step 504 of FIG. 15 is performedwhere the distance field value for current voxel 600 is set to thesmaller of the two Z-buffer values for the current voxel. In particular,the magnitudes of the Z distance value in the +Z-buffer and −Z-bufferare compared and the smaller magnitude is set as the distance fieldvalue for the current voxel. In addition, the sign of the distance fieldvalue is set based upon whether the voxel is inside or outside of thepart. If the voxel is inside the part, the distance field value is setas a positive value and if the voxel is outside of the part, thedistance field value is set to a negative value.

At step 506, a ring of voxels around the current voxel in the currentslice is identified. For example, in FIG. 16 , a first ring 602indicated by the dotted shading surrounds current voxel 600. At step508, a voxel in the identified ring is selected. If this selected ringvoxel is at the STL boundary at step 510, the distance between theselected ring voxel and the current voxel 600 is used as a testdistance. If the ring voxel is not at the STL boundary, a combination ofthe smaller of the two Z-buffer values for the ring voxel and thedistance between the ring voxel and the current voxel is used todetermine the test distance at step 514. In particular, the Z-buffervalues in the +/−Z-buffer for the ring voxel are compared to each otherand the smaller magnitude of the two Z-buffer values is selected as avertical component of the distance to the part. A horizontal componentof the distance of the part is computed as the distance between the ringvoxel and the current voxel 600. Squaring the vertical component of thedistance and the horizontal component of the distance, summing thesquares, and taking the square root of the sum provides the distancebetween the current voxel 600 and the portions of the part above orbelow the ring voxel. Note that if no portion of the part is above orbelow the ring voxel, the Z-buffers will each contain large magnitudevalues.

The test distance value computed in either step 512 or 514 is thencompared to the current stored distance field value for the currentvoxel 600 at step 516. If the test distance is less than the currentdistance field value, the test distance is set as the new currentdistance field value. If the magnitude of test distance is not less thanthe magnitude of the current distance field value, the current distancefield value remains the same.

At step 518, the method determines if the ring voxel is at thesilhouette boundary, such as silhouette boundary 610 of FIG. 16 . If thering voxel is at the silhouette boundary, a shortest distance to thesilhouette boundary for current voxel 600 is set to the lesser of apreviously stored distance to the silhouette boundary for current voxel600 and the distance between the ring voxel and the current voxel atstep 520. Thus, if the ring voxel is at the silhouette boundary and thedistance between the ring voxel and the current voxel is smaller thanpreviously identified distances between the current voxel and thesilhouette boundary, the shortest distance between the current voxel 600and the silhouette boundary is updated to reflect the distance betweenthe ring voxel and the current voxel 600.

If the ring voxel is not at the silhouette boundary or after thedistance to the silhouette boundary has been updated, the process ofFIG. 15 determines if there are more ring voxels in the current selectedring. If there are more ring voxels, the process returns to step 508 andthe next voxel in the current ring is selected. Steps 510-522 are thenrepeated. When all of the voxels in a current ring have been processedat step 522, the method determines if there are more voxels around thecurrent ring at step 524. If there are more voxels around the currentring at step 524, the process returns to step 506 and the next ringaround the current ring of voxels is selected. For example, after ring602 is processed, ring 604 is processed, then ring 606, then ring 608.In processing successive rings, the STL boundaries are not crossed. Assuch, once an STL boundary is reached, voxels on the other side of theboundary are not processed. For example, voxel 652 is not processed aspart of ring 608 since STL boundary 612 separates voxel 652 from currentvoxel 600. The same is true for rings of voxels that are processedwithin a part. Specifically, when a current voxel is located within apart, voxels outside of the part are not used to determine the distancefield for the voxel.

When there are no more voxels around the current ring at step 524, theprocess ends and the distance field value stored for the current voxelis output as the final distance field 9212 (FIGS. 10 and 12 ). Thisdistance field value will have a magnitude representing the shortestdistance between the current voxel and any STL boundary of the part anda sign that will indicate whether the current voxel is within the partor is exterior to the part. In addition, when the distance field valueis updated for the current voxel, one or more features associated withthe distance field value are also stored such as the position of theclosest point on the STL boundary, identifiers of the body or mesh thatthe closest point is located on, surface texture coordinates, and thesurface normal at the closest point, for example. In accordance with oneembodiment, different features of the part have different sets ofmaterial selection rules associated with them. As a result, differentportions of the part can have different material selection rulesassociated with it. Similarly, the shortest distance to the silhouetteboundary 9216 is output as is the location of the closest silhouetteboundary point 9218.

When there are multiple parts in build space 400, the steps of FIG. 15are repeated for each part to generate a distance field value 9212, aclosest STL boundary point 9214, a closest distance to the silhouette9216 and the closest silhouette boundary point 9218 for the voxel foreach part. It is possible for a single voxel to be outside of all parts,to be located in a single part while outside of other parts, or to belocated within multiple parts.

Returning to FIG. 11 , after the distance field values and the distanceto the silhouette boundary have been determined for the selected voxelat steps 9114 and 9116, respectively, material for the voxel isdetermined at step 9118 by a material selection unit 9226. FIG. 17provides a flow diagram showing initial steps in performing the materialselection.

At step 9700, the distance fields are examined to determine if the voxelis in at least one part. This determination can be made by determiningif there is at least one non-negative distance field value stored forthe voxel. If the voxel is in at least one part, all negative distancefield values for the voxel are ignored at step 9702. Thus, if a voxel islocated within at least one part, the material selection rules 9220associated with the voxel being inside part(s) control the materialselection and the material selection rules 9220 associated with thevoxel being outside of other parts are ignored. Note that if there isonly one part in the build space, there will be no negative distancefields to ignore at step 9702.

At step 9704, material selection unit 9226 determines if there aremultiple parts in the build space. If there is only one part in thebuild space, a single-part material selection process is performed atstep 9706. An example of one such single-part material identificationprocess is discussed further below. If there are multiple parts at step9704, a multipart material selection process is performed at step 9708.One example of such a multipart material selection process is discussedbelow.

Returning to step 9700, if the voxel is not in any of the parts in thebuild space, the voxel's position relative to the silhouette boundary isexamined at step 9710 to determine if the voxel is in a direct supportregion for a part. A direct support region is a region in the buildspace located within a silhouette of a part. Such direct support regionsrequire sufficient support material to support the part as it is built.Determining whether a voxel is in a direct support region involveslooking at the +Z-buffer value(s) for the voxel. If any of the +Z-buffervalue(s) is negative and has a magnitude less than the maximummagnitude, the voxel is in a direct support region. If the voxel is in adirect support region, a direct support designation is set at step 9712for the voxel.

If the voxel is not in a direct support region at step 9710, the voxel'sposition is examined to determine if it is in an angled support regionfor the part at step 9714. For some parts, in addition to providingadditional support in the direct support regions, additional support isalso provided outside of the silhouette of the part so that theadditional support has an angled surface and is not completely vertical.To determine if the voxel is in an angled support region for the part,the distance to the closest silhouette boundary for the part is combinedwith the vertical distance to the part from that closest point on thesilhouette boundary to determine an angle between the voxel and theportion of the part above the silhouette boundary relative to the xyplane of the slice. If this angle is greater than some maximum angle setfor the angled support region, the voxel is considered to be within theangled support region at step 9714. If the computed angled is less thanthe maximum angle for the angled support region, the voxel is consideredto be outside of the angled support region for the part. If the voxel iswithin the angled support region at step 9714, a designation that thevoxel is in the angled support region is set at step 9716. After step9714 or step 9716, the process moves to step 9704 to determine if thereare multiple parts in the build space.

FIG. 18 provides a diagram showing a full support region 800, an angularsupport region 802 and a fill support region 804 for a part 806. Fullsupport region 800 includes areas outside of the part that are withinsilhouette boundary 810 of the part. Angular support region 802 includesareas that are within an angle 812 of point 814 of the part atsilhouette boundary 810. Full support region 800, angular support region802 and fill support region 804 can each include different materialsand/or different modulating functions from each other. In general, fullsupport region 800 will include materials and modulating functions thatprovide more support than fill support region 804. Angular supportregion 802 can include the same materials and modulating functions asfull support region 800 or may include different materials or modulatingfunctions.

FIG. 19 provides a flow diagram for performing step 9706 of FIG. 17 inwhich a material identification is performed with respect to a singlepart in the build space. At step 900 of FIG. 19 , point features for theclosest portion of the part to the voxel are retrieved from pointfeatures 9209 by material selection unit 9226. These point features areused to identify a set of material selection rules 9220 to be used whendetermining the material for voxels near the part portion. In accordancewith one embodiment, the set of material selection rules contains aseparate material selection rule 9224 for each of a set of ranges 9222of distance field values. In accordance with some embodiments, eachmaterial selection rule is one of a static rule that assigns a samematerial at a same density across the entire range of distance fieldvalues, and a modulating rule that varies the composition of the voxelsacross the range of distance field values.

At step 902, material selection unit 9226 retrieves the sets of materialselection rules identified in the point features and at step 904 usesthe distance field and the region designation (i.e. direct supportregion, filler region), if any, for the voxel to identify which materialselection rule to use.

In accordance with one embodiment, ranges 9222 describe bands ofmaterials relative to the STL boundary where each band has an associatedmaterial selection rule 9224. Within a range 9222, the materialselection rule 9224 can simply designate a single material to use withinthe range. For other ranges, the material selection rule 9224 consistsof one or more functions that are evaluated to produce output values.Groups of output values are assigned to different material designations.For example, some output values of the functions can be assigned to afirst material while other output values are assigned to a secondmaterial. Other times, one group of output values is assigned to amaterial while the remaining output values are assigned to no material,meaning that no material is placed in the voxel. For example, inaccordance with one embodiment, the following bands and functions aredefined:

-   -   for a>D>b    -   f(x, D)>0→material designation 1    -   f(x,D)<0→material designation 2    -   f(x,D)=0→material designation 3    -   for b>D>0    -   g(x,D)>0→material designation 4    -   g(x,D)<0→material designation 5    -   g(x,D)=0→material designation 6    -   for D=0    -   h(x)>0→material designation 7    -   h(x)<0→material designation 8    -   h(x)=0→material designation 9    -   or 0>D>−c and direct support    -   k(x, D)>0→material designation 10    -   k(x, D)<0→material designation 11    -   k(x, D)=0→material designation 12    -   for 0>D>−c and angled support    -   l(x,D)>0→material designation 13    -   l(x,D)<0→material designation 14    -   l(x,D)=0→material designation 15    -   for 0>D>−c and nonshine    -   m(x, D)>0→material designation 16    -   m(x, D)<0→material designation 17    -   m(x,D)=0→material designation 18    -   for 0>D>−c and shine    -   n(x,D)>0→material designation 19    -   n(x,D)<0→material designation 20    -   n(x, D)=0→material designation 21    -   for −c>D>−d and direct support    -   o(x,D)>0→material designation 21    -   o(x,D)<0→material designation 22    -   o(x,D)=0→material designation 23    -   for −c>D>−d and angled support    -   p(x,D)>0→material designation 24    -   p(x,D)<0→material designation 25    -   p(x, D)=0→material designation 26    -   for −c>D>−d and otherwise    -   q(x,D)>0→material designation 27    -   q(x,D)<0→material designation 28    -   q(x, D)=0→material designation 29

where D is the distance field value, a, b, −c and −d are range valuesfor the distance field values, x is the three-dimensional location ofthe voxel in the build space, f(x, D), g(x, D), h(x, D), k(x, D), l(x,D), m(x, D), n(x, D), o(x, D), p(x, D), and q(x, D) are modulatingfunctions and material designations 1-29 are possible materials and nomaterials to be used for the voxel. Although listed as separatematerials 1-29, those skilled in the art will recognize that one or moreof the material designations may be the same.

The modulating functions can be periodic or aperiodic functions of oneor more features of the voxel such as the voxel's position in the buildspace, or the distance field D for the voxel. For periodic functions,the position in the build space or the distance field or a combinationof these two values can be used to control the frequency of the periodicfunction, a temporal shift in the periodic function and/or the magnitudeof the periodic function. The modulating function can also be a noisefunction based on the voxel's position in the build space or based onthe distance field. In further embodiments, the modulating function is acombination of a periodic function and a noisy function. For example, inone embodiment, the periodic function is based on both the position inthe build space and the distance field and the output of the periodicfunction is filtered by a noisy filter based on the voxel's position inthe build space. In a still further embodiment, the modulating functionis the sum of the distance field value and a base periodic function ofthe voxel position in the build space.

In the examples above, three ranges of values for the functions havebeen described with three associated material designations. When themodulating function provides a constant value, only a single materialwill be identified producing a band of solid material across the rangeset by the distance field. In other embodiments, other ranges of valuesfor output of the modulating function are used allowing for any numberof materials to be used within the range of distance field values setfor the modulating function. In further embodiments, one or more of theranges of values for the modulating function can be associated withempty space resulting in no material being assigned to the voxel. Forexample, it is possible to assign a material when the output of themodulating function is greater than or equal to 0 and to assign an emptyspace to the voxel when the output of the modulating function is lessthan 0. This allows a porous band of material to be constructed with theporosity of the material changing as a function of the distance fieldand/or the position in the build space.

The frequency of the modulating function can change as a continuousfunction of the distance field or can be fixed at the value of thedistance field at the beginning or the end of the range of distancefields associated with the modulating function. Similarly, the amplitudeof the modulating function can similarly vary continuously as a functionof the distance field values or can be set to the value of the distancefield at the beginning or ending range of distance field valuesassociated with the modulating function.

As shown in the example set of material selection rules above, theselection of a material selection rule can also be based upon whetherthe voxel is located in a direct support region or an angled supportregion as designated for the voxel in step 9712 and 9716 above. Inaddition, shine maps 9208 can be consulted for the portion of the partclosest to the voxel to determine whether that portion of the part is tohave a particular shine level. This shine level can then be usedtogether with the distance field to select the material selection ruleto apply to the voxel.

Returning to FIG. 19 , at step 906, the distance field value of thevoxel and/or the build space position of the voxel are applied to theselected material selection rule to select a material or no material forthe voxel. In some embodiments, as shown above, the material selectionrule 9224 is a function of a feature of the voxel, such as the distancefield value or the build space position of the voxel, and the distancefield value and or the build space position of the voxel are applied tothe function to generate an output value that is then used to select thematerial or lack of material for the voxel.

If there is more than one part in the build space, a multipart materialselection is performed at step 9708 of FIG. 17 . FIG. 20 provides a flowdiagram of one method for performing a multipart material selection.

At step 1000, material selection unit 9226 accesses point features 9209to retrieve the features for the closest STL boundary points 9214 forthe multiple parts. These features are then used to determine whetherthe material selection rules designated for the STL boundary point areto be blended with the material selection rules for STL boundary pointsof other parts or whether a selection is to be made between the materialselection rules of the various parts so that only a single part'smaterial selection rules are used.

If only a single part's material selection rules are to be used, theprocess continues at step 1002 where one of the parts is selected usingthe closest STL boundary points of the various parts. In particular, thefeatures 9209 of the closest STL boundary points will indicate which ofthe parts is to be given priority when selecting a set of materialselection rules. After the part with priority has been selected at step1002, single part material selection is performed at step 1004 using theprocess described above for FIG. 19 .

FIG. 21 provides an example of a top cross-sectional view of a partconstructed using the single part construction process of FIG. 19 . InFIG. 21 , the part is defined by an STL boundary 1100 that is dividedinto two regions 1102 and 1104, each having respective features. Forregion 1102, three bands of material selection rules are defined outsideof the part and four bands of material selection rules are definedinside the part. In particular, outside of the STL boundary there is aband 1106 constructed by a modulating function that modulates betweenproducing two different materials resulting in a support area withstructure. Band 1108 includes an aperiodic modulating function thatprovides a constant amount of a single support material. Band 1110consists of an aperiodic modulating function that assigns an air gap tothe voxels in the band. Within the STL boundary, band 1112 isrepresented by an aperiodic modulating function that provides a constantdensity coating material. Band 1114 is described by a modulatingfunction that modulates between the coating of band 1112 and a corticalmaterial found in a cortical band 1116. Cortical band 1116 has a varyingthickness as indicated by wider thickness 1118 and narrower thickness1120. Thus the size of cortical band 1116 varies based on what is theclosest STL boundary point. Cortical band 1116 is described by anaperiodic modulating function that provides a constant intensitycortical material. Band 1122 is described by a noisy modulating functionthat modulates between the cortical material of band 1116 and a marrowmaterial. The noisy function increases the amount of marrow material asthe distance field increases.

Region 1104 contains bands 1106 and 1108 from the exterior of region1102 but only includes interior band 1122 from region 1102.

Returning to FIG. 20 , when the point features 9209 for the closest partpoints indicate that the material selection rules of two different partsare to be blended at step 1000, the process continues at step 1006. Instep 1006, at least two of the parts in the build space are selected.The number of parts that are selected is based on designations stored inpoint features 9209 for all of the parts in the build space. Suchfeatures can include threshold distance fields that require the voxel tobe within a certain distance of the STL boundary in order for the part'smaterial selection rules to be used during blending. In otherembodiments, certain point features 9209 will indicate that a part'smaterial selection rules are only to be blended when a certain number ofother parts are present in the build space.

At step 1008, material selection rules 9220 associated with the partsselected at step 1006 and identified in point features 9209 areretrieved. At step 1010, the respective distance field of the voxel andregion designation, if any, of the voxel relative to each part selectedat step 1006 are used to identify which material selection rules are tobe selected for blending. At step 1012, one or both of materials andmodulating functions of the selected material selection rules areblended or merged. In accordance with one embodiment, blending ormerging modulating functions involves weighting the modulating functionsusing the distance fields and summing or multiplying the weightedmodulating functions to form a merged function. The weighting is suchthat if a voxel is within two parts, the weight for a modulatingfunction of one of the parts increases as the distance field value forthat part increases. When the voxel is located outside of two parts, theopposite is true and the weighting for the modulating function relativeto a part decreases as the magnitude of the distance field for the partincreases. In other embodiments, the blending or merging is performed byusing a random function and selecting which material to apply based onwhether the output of the random function is above or below a threshold.The threshold is set as a function of the distance field for one of theparts, such that it becomes more likely that a material of a particularpart will be selected for the voxel as the distance field for that partincreases. This produces a merged area across the overlapping portionsof the two parts where the material content of the voxels changesgradually across the merged area.

After the material/modulating functions have been blended at step 1012,the distance fields for one or more of the parts are applied to theblended functions at step 1014 along with the build space region for thevoxel to produce a computed value that is then used to select thematerial for the voxel at step 1016.

FIG. 22 provides an example of multiple part material selection in whichselecting a single part at step 1002 removes interference between parts.At times, meshes 9202 for different parts will be described such thatthe parts overlap when the designer intended the parts to be separate.Such interference can be time consuming to remove. Under step 1002, suchinterference is automatically eliminated by selecting only one of theparts when a voxel is described by meshes 9202 as being in two differentpart.

In the example of FIG. 22 , there are two parts 1200 and 1202. Dottedlines 1204 indicate the STL boundary for part 1202 as described bymeshes 202 and solid line 1205 indicates the STL boundary for pat 1200.As shown in FIG. 22 , STL boundary 1204 is within part 1200 and as such,the description of the STL boundaries shows an interference betweenparts 1200 and 1202. By selecting a single part at step 1002, in thiscase, part 1200, it is possible to remove the interference described inthe meshes 202 to provide a new part boundary 1206 (shown in bold) forpart 1202. Thus, in interference area 1208 where parts 1200 and 1202overlap, the selection of part 1200 at step 1002 effectively shiftsboundary 1204 to boundary 1206 for part 1202, thereby eliminating theinterference between the two parts.

FIG. 23 provides an example of blending two modulating functions using adistance field. In FIG. 23 , a gyroid modulating field shown in section1300 is blended with a Schwartz lattice as shown in section 1302 acrossa blending area 1304. In the blending of FIG. 23 , the two modulatingfunctions are weighted such that as the distance field from the STLboundary defining the gyroid increases, the gyroid modulating functionis weighted less and the Schwartz lattice is weighted more. Thisproduces a smooth transition from the gyroid lattice to the Schwartzlattice.

FIG. 24 shows the blending of parts material across an overlappedportion of two parts 1400 and 1402. In blended region 1404, the amountof material associated with part 1400 gradually decreases and the amountof material associated with part 1402 gradually increases along theextent from part 1400 to part 1402. Thus, as the magnitude of thedistance field for part 1400 decreases, the amount of part material forpart 1400 decreases in the blended region. Similarly, as the distancefield for part 1402 decreases along the blended region 1404, the amountof material associated with part 1402 decreases in the blended region.

Returning to FIG. 11 , after the material for a voxel has beendetermined at step 9118, the process determines if more voxels need tobe processed at step 9120. If there are more voxels in the currentslice, a new voxel is selected by returning to step 9112 and steps 9114,9116, and 9118 are repeated for the new voxel. When all of the voxelsfor the current slice have been processed at step 9120, the materialbitmap for the slice is complete and is output as material bitmap 9228.At step 9122, the process determines if there are more slices. If thereare more slices, slice computations process 9210 moves up one slice atstep 9124 and then returns to step 9106 to perform rendering operationsin the +Z direction for the new slice. Steps 9108, 9110, 9112, 9114,9116, 9118, and 9120 are then repeated for the new slice. Note thatalthough the selection of materials for each voxel in a slice has beenindicated as being performed before the +Z-buffer is loaded for eachslice, and other embodiments, the rendering operation is performed inthe +Z direction for each slice before determining materials for thevoxels in any of the slices. After the +Z-buffers have been loaded foreach slice, each slice is processed in turn by material selection unit9226 to identify the material for each voxel in the slice.

After material bitmaps 9228 have been formed for each slice, a printconversion unit 9230 performs a print conversion step 9126 to form printinstructions 9237. This print conversion step can be as simple astransferring material bitmaps 9228 as bitmaps 9232. In otherembodiments, material bitmaps 9228 are converted into toolpaths 9234that describe how a print head should be moved along a slice to depositmaterial. In one embodiment, a marching square algorithm is used toidentify toolpaths 9234 from bimaps 9228. In a further embodiment, thematerial bitmaps 9228 for each slice is converted into meshes 9236 thatprovide three-dimensional descriptions of part boundaries. Such meshescan be applied as input to other printers or as input to CAD systems. Inone embodiment, a marching cubes algorithm is used to identify meshes9236 from bitmaps 9228. After the material bitmaps 9228 have beenconverted into print instructions 9237, the print instructions arecommunicated through communication adapter 9092 so that the part can bemanufactured at step 9128.

The embodiments above can thus load a CAD model onto a GPU, use the GPUto compute signed distance fields for every voxel, assign a material toeach voxel based on the signed distance fields, and outputs imagessuitable for printing.

The various embodiments compute several different distance fields foreach voxel in a slice, including the 3D Euclidean distance to theclosest point of the CAD model, the 2D distance to the closest point onthe cross section of the model in the slice, and the 2D distance to thesilhouette of the model.

Each distance field may include feature transform information for thevoxel, where the feature is the source point on the model used to recordthe distance reported for that voxel in the distance field. Featuretransforms may include identifiers of the body or mesh, surface texturecoordinates, surface normal, and position of the source point.

In accordance with one embodiment, the material assignment to each voxelbecomes a function of the distance information and user-controlledparameters.

The distance metric may be Euclidean norm or a different norm, such as aL^(p) or a chamfer norm.

The computations on the GPU use the Z-buffer to produce the depthcomponent of distance in planar projections.

The computations on the GPU use a distance transform to compute 3Ddistance, 2D sectional distance, or distance from self-supportingregions.

The distance fields can be used to modulate carrier functions, such asimplicit lattices and noise functions, to produce structures withvarying compliance and porosity.

The distance fields can be used to perform offsetting and booleanoperations.

The distance fields can be used to smoothly interpolate from one CADmodel to another.

The distance fields can be used to adjust interferences and gaps betweenparts.

The distance fields can be used to create variable thickness offsets.

The distance fields can be combined with surface and volumetric texturesto create layered and rippled textures.

The distance fields can be combined with voxel data, such as CAT scanand MRI data to produce models with volumetrically varying materialproperties.

The results can be saved as bitmap images for use for printers that useimages.

The results can be traced into vector contours for 3D printers that usetoolpaths.

The results can be reconstructed into 3D solid models.

The computations on the GPU use convolution or sampling to compute 2Dsectional distance, silhouette distance, and the planar components of 3Ddistance. In accordance with one embodiment, these computations areperformed iteratively to recursively compute distances efficiently.

The distance information can be used to modulate explicit and implicitfunctions, such as those describing lattices, to produce structures withvarying bulk material properties such as compliance and porosity. Thefunctions may describe shapes, voids in shapes, textures, varyingmaterial properties, and beam-like, honeycomb, and mixed topologylattices.

In the embodiments described below, there are CPU and GPU components.The CPU component:

-   -   1. Reads mesh data, textures, and slicing parameter data.    -   2. Sends the mesh data and related information to the GPU.    -   3. Provides a user interface to view and interact with the slice        data.    -   4. Saves images created on the GPU to disk.

The GPU component:

-   -   1. Produces depth information about the model using the        Z-buffer.    -   2. Combines the depth information into structures with different        distance information.    -   3. Calculates the composition of each voxel using the distance        information.    -   4. Includes libraries for calculating lattices, performing solid        modeling operations, calibrating color, etc.

In one embodiment, the various embodiments are implemented usingJavascript, Node.js and Electron for the CPU and OpenGL ES for the GPUcode. Other embodiments are implemented using C# on .NET or Mono andOpenGL 3.3.

Additional Applications:

-   -   1. Recording texture, normal, and other geometric information        (collectively, “Surface Information”) along with distance        information while computing the distance field.    -   2. Using Surface Information and a bitmap to choose a color to        assign to the model.    -   3. Using Surface Information and a bitmap to choose a material        among several possible materials, possibly using dithering.    -   4. Using Surface Information and a bitmap to offset the model to        create a physical displacement map.    -   5. Using Surface Information and a bitmap to change the        glossiness of the printed result.    -   6. Using Surface Information and a bitmap to change the surface        finish of the printed result.    -   7. Using Surface Information and a bitmap to change the hardness        of the material closest to the value of the texture on the        surface.    -   8. Using Surface Information and a bitmap to change the        transparency of the material closest to the value of the texture        on the surface.    -   9. Using Surface Information and a bitmap to change the        mechanical properties, such as stiffness, of the material        closest to the value of the texture on the surface.    -   10. Using Surface Information and a bitmap to alter the presence        of support material on the surface of a part.    -   11. Using Surface Information and a bitmap to modulate implicit        functions used in the volume of the part or in support        structures surrounding it.    -   12. Using Surface Information and several bitmaps to produce        several displacement maps that can be combined via Boolean        operations to create surface textures that include overhang.    -   13. Using Surface Information and several bitmaps with        transparent material to produce lenticular (animated or 3D)        surface effects.    -   14. Using any combination of 2-9 together.    -   15. The use of 3D volumetric textures with distance field        information to change material location composition, possibly in        combination with 2-9.

In FIG. 9 , computer 9066 was shown as a host for a single stand-aloneadditive manufacturing system. Alternatively, computer 9066 may functionas a local server for multiple additive manufacturing systems 9068. Forexample, systems 9068 may be part of an overall production system tomanufacture consumer or industrial OEM products. As such, computer 9066and may perform the steps of FIG. 11 and may also perform one or moreadditional processing steps, such as run-time estimates, printerqueuing, post-processing queuing, and the like. As shown, computer 9066may optionally include one or more servers 9072 and one or morededicated host computers 9074 associated with each system 9068, whereserver 9072 may communicate with host computers 9074 over one or morecommunication lines 9076 (e.g., network lines).

In yet another embodiment, computer 9066 and systems 9068 may be part ofan on-demand service center. In this embodiment, computer 9066 mayfunction as a cloud-based server, for example, where customers maysubmit digital models (e.g., STL data files) from their personalcomputers 9078 over the Internet via one or more network orcommunication lines 9080 to computer 9066 (e.g., to server 9072).

In this application, computer 9066 may perform the steps of FIG. 11 aswell as one or more additional processing steps, such as supportmaterial volume calculations, price quoting, run-time estimates, printerqueuing, post-processing queuing, shipping estimates, and the like. Forexample, in some embodiments, computer 9066 may generate supportmaterial volume calculations, build times, and price quoting asdiscussed in Nehme et al., U.S. Pat. No. 8,818,544. The service centermay also include one or more post-printing stations (e.g., supportremoval stations, surface finishing stations, shipping stations, and thelike, not shown), where computer 9066 may also optionally communicatewith the post-printing station(s).

According to some embodiments of the invention there is provided amethod comprising: selecting a voxel in a three-dimensional build space;for the selected voxel, determining a distance field value relative to athree-dimensional part in the three-dimensional build space; using thedistance field value to select at least one material selection rule;applying a feature of the voxel to the at least one material selectionrule to identify a material designation for the voxel, wherein thematerial designation indicates no material is to be placed at the voxelwhen the material selection rule identifies no material for the voxeland wherein the material designation indicates at least one material isto be placed at the voxel when the at least one material selection ruleidentifies the at least one material for the voxel; and outputting thematerial designation for the voxel for use in building thethree-dimensional part using an additive manufacturing system.

According to some embodiments of the invention the method uses theshortest distance to determine the distance field value.

According to some embodiments of the invention the distance field valueis in a first range of values if the voxel is outside of the part, is ina second range of values if the voxel is within the part and is asingular value if the voxel is on the boundary of the part.

According to some embodiments of the invention the voxel forms part of alattice structure.

According to some embodiments of the invention the using the firstdistance field value and the second distance field value to set amaterial designation comprises using the first distance field value toidentify a first function, using the second distance field value toidentify a second function, merging the first function with the secondfunction to form a merged function, and using the merged function to setthe material designation.

According to some embodiments of the invention the first functiondescribes a first lattice pattern, the second function describes asecond lattice pattern and the merged function describes a transitionlattice that transitions from the first lattice pattern to the secondlattice pattern over a merge area.

According to some embodiments of the invention the using the firstdistance field value and the second distance field value to set amaterial designation comprises using the first distance field value todetermine that the voxel is inside the first three-dimensional part,using the second distance field value to determine that the voxel isinside the second three-dimensional part and setting the materialdesignation for the voxel to a material set for the firstthree-dimensional part instead of a second material set for the secondthree-dimensional part.

According to some embodiments of the invention the setting the materialdesignation for the voxel to the material set for the firstthree-dimensional part instead of the second material set for the secondthree-dimensional part comprises identifying a closest portion of thefirst three-dimensional part to the voxel, retrieving a featureassociated with the closest portion, and using the feature to decide toset the material designation for the voxel to the material set for thefirst three-dimensional part.

Example 5 Experimental Tests

A few synthetic geometries have been printed by the following 3D inkjetprinters: J750 and Connex3 (Stratasys Ltd., Israel). These includedstraight tubes having inner diameter (I.D.) of from about 1 mm to about20 mm and wall thicknesses of from about 0.5 mm to about 2 mm, curvedtubes, jigs, heart coronaries and aorta, circle of Willis stroke mode,and Theresa's Aneurysm. FIGS. 29A-29D are visualized computer objectdata (FIG. 29A) and images (FIGS. 29B-29D) of tubes array (FIG. 29A)printed tubes of varying composition (FIG. 29B), linear and curved tubegeometries (FIG. 29C), and Theresa Aneurysm (FIG. 29D).

At the first stage all parts were initially printed using the buildingmaterials “Agilus™ 30” (as an elastomeric curable formulation) and“SUP706” (as a curable support material formulation) (Stratasys Ltd.,Israel). Generally, all simple geometries were easily cleaned viawater-jet without injuring the tube. The tube expands under waterpressure and the support detached and was pushed out.

Agilus™30 tubes with 3 mm wall thickness and 16 mm outer diameter (O.D.)were used as a benchmark and compared to tubes made of the buildingmaterial “Tango™+” (Stratasys Ltd., Israel). In this test the tubes wereexpanded using an insert to 110%, 120%, 130%, 140% and 150%. Table 5.1below lists the time to failure for sets of 3 specimens.

TABLE 5.1 10% 20% 30% 40% 50% Agilus ™30 More than 2 to 3 4:20 2:15 0:457 days days Tango ™+ — 7 min Less than Less than — 1 min 1 min

This test demonstrates that Agilus30 has a superior performance inresisting stress.

Effect of Tube Geometry

Test specimens were tubes with four 90 degree bends at X-Y and X-Zplanes. Straight tubes of the same length and diameters were used as areference. Burst pressures for straight tubes were in the range of1.5-1.7 bars. Curved tubes stood up to 1.2-1.3 bars.

Effect of Wall Thickness

This test was conducted on Agilus™30 tubes with a length of 60 mm withvarying wall thickness to check for max momentary pressure sustainablefor each wall thickness. The results are listed in FIG. 30 and Table 5.2below.

TABLE 5.2 Wall Max Thickness pressure [mm] [bar] 0.8 0.9 1 1.2 1.2 1.61.6 2 2 2.1

The thicker wall thickness improves the tube resistance to pressure,initially in a linear manner, but above 1.5 mm getting to a plateau. Inthis experiment the compliance was not recorded.

Tensile Test of Tube-Shaped Geometry

This test included a specimen made of Agilus30™ Clear (Stratasys Ltd.,Israel) material, with a Vero White (Stratasys Ltd., Israel) clampingsurface to be used for tensile test on Lloyd instrument. The specimenstructure was a tube of an O.D. of about 8 mm with 1 mm wall thickness,which translates to a cross-section surface of 21.98 mm² with a lengthof 100 mm. FIG. 31 is a graph below represents Stress vs Strain Curves.The strength of the tube is about 1 MPa, which is about one third of thestrength seen when using a standard dog bone sample.

This experiment suggests that the tube is weaker than a glossyrubber-like dog bone printed in XY orientation. It is assumed that thisis due to the vertical matte surfaces characteristics.

Reinforcement with RGD515+

In this experiment the effect of reinforcement with the buildingmaterial RGD515+(Stratasys Ltd., Israel) was tested.

Specimens of I.D.=8 mm, O.D.=10 mm and L=60 mm, were used. All testswere conducted under constant, regulated pressure of 1 bar. The modelsspecimens printed together, including reference models, at XYorientation. DMs of Agilus™30 with 2% to 10% of RGD515+, at randominterlacing, were employed. FIGS. 32A-32C and Tables 5.3A and 5.3B, listthe measured and calculated values for these tubes.

TABLE 5.3A Time to failure Radial Axial RGD515+ @ 1 bar expansionexpansion Anisotropy content [m] [%] [%] ratio  0% 2.5 108.5 67.4 0.62 2% 2.5 84.3 30.8 0.37  4% 0.6 36.3 11.6 0.32  6% 0.4 8.8 7.5 0.85  8%11.8 18.6 4.0 0.22 10% 6.7 12.2 2.0 0.16

TABLE 5.3B Initial Lumen I.D. @ lumen area @ RGD515+ 1 bar area 1 barcontent [mm] (mm{circumflex over ( )}2) (mm{circumflex over ( )}2)Compliance  0% 16.00 21.98 47.10 1.14  2% 14.80 21.98 43.33 0.97  4%10.90 21.98 31.09 0.41  6% 8.70 21.98 24.18 0.10  8% 9.37 21.98 26.280.20 10% 8.85 21.98 24.65 0.12

The results demonstrate that small percentage of RGD515 reduces thestrength and durability of the tube, but at 8% and above the durabilityincreases. The results also demonstrate that the compliancesignificantly decreases and reach a plateau after 6% RGD515+. Theresults also demonstrate that the expansion is anisotropic, wherein theaxial expansion is larger than the radial expansion, while the gapbetween them decreases with increasing percentage of RGD515.

Softening

A significant softening and increase in compliance was observed when thesoft modeling formulation described in Example 1 was added. It was addedas an inner layer and was encapsulated in Agilus™30. Such a tube canhold a pressure of up to 0.4 bar.

Oriented Reinforcement

FIG. 33 illustrates oriented reinforcing elements that were used in thistest. The reinforcing elements were made of RGD515+ and where embeddedin an Agilus™30 shell. Tests were directed to measuring the time torupture at constant strain and constant pressure. The results areprovided in Tables 5.4A and 5.4B.

TABLE 5.4A Constant Strain 10% 20% 30% 40% 50% Agilus ™30 More than 2 to3 4:20 2:15 0:45 7 days days Coil reinforced — — — 24 H more Agilus ™30than 5 H

TABLE 5.4B Time to failure Axial Radial @ 1.4 bar Expansion ExpansionConstant Stress [min] [%] [%] Agilus ™30 ref 1.5 Fibers 17.4 ~0 27.4Ribs + fibers >60 ~0 13.5 Ribs 8.2 41.33 13.8

The results demonstrate the superior effect of coil reinforcement ondurability at constant strain and the positive effect of otherreinforcement types on durability at constant stress. The data alsovalidates a highly anisotropic behavior for Ribs reinforcement.

Wetting

This test was aimed to check whether there is a significant change inthe ability of the printed tubes to sustain pressure after introduced towater for a large period of time.

Three Agilus™30 tubes of different size were submerged in water for 48hours and to dry tubes. The immersion in water altered the materialcolor to an almost opaque white. Time sustained at 1 bar pressure waschecked for each set of tubes. The results are provided in Table

TABLE 5.5 Time @ 1 Bar 1st 2nd 3rd [m] sample sample sample Avg. StdevWet 1.0 2 1.6 1.5 0.39 Dry 0.8 1.7 1.1 1.2 0.37

The results demonstrate that the wet tube showed no change in thisaspect.

Encapsulation

In this test, a performance evaluation regarding pressure holdingcapability was held. Three wall thickness were checked: 0.3, 0.4 and 0.5mm with an O.D. of 8 mm. The encapsulated vessel specimen areillustrated in FIGS. 34A and 34B. Tubes with no encapsulation were alsoprinted as a reference. All specimens were printed with liquid support.The results showed that encapsulated tubes with 0.3 and 0.4 mm wallthickness sustained the pressure of 0.4 bars or less. 0.5 mm wallthickness model was sustained a pressure of 0.7 bars. The referencemodels cracked during handling/printing, and were very brittle.

Hardened Support and Liquid Support

The support formulation SUP707 (an exemplary gel or gel-like supportformulation) (Stratasys Ltd., Israel) has a negative effect on thedurability of tubes, as indicated in Table 5.6.

TABLE 5.6 SUP706 Time to Linear Radial failure Expansion Expansion @ 1bar [mm] [%] [m] 10.01 66.83 3.33 9.11 51.83 4 9 50 3.33 8.88 48 3Average 9.3 54.2 3.4 St. Dev. (%) 5.6 15.9 12.3 SUP707 Time to LinearRadial failure Expansion Expansion @ 1 bar [mm] [%] [m] 9.11 51.83 1.349.18 53 0.5 9.61 60.17 0.3 8.85 47.5 1 Average 9.2 53.1 0.8 St. Dev. (%)3.4 9.9 60.2

Specimens of 1 mm wall thickness with an O.D. of 6 mm were tested underconstant air pressure of 1 bar. 3 types of support were tested: regularSUP706, 1 mm Sup 706 outer layer and full liquid support (a formulationthat provides, upon exposure to a curing condition, a liquid orliquid-like material, e.g., as described in Example 2). The results aresummarized in Table 5.7.

TABLE 5.7 Time to failure @ 1 Bar (min) Liquid support 3:53 1 mm 706layer 5:27 SUP 706 6:30

The results demonstrate that although the liquid support has a negativeeffect on the tube performance, the amplitude of the decrease ismoderate and is significantly reduced by the coating with 1 mm ofSUP706.

Compliance

In this study the compliance was measured according to the followingmeasurement protocol:

-   -   1. Connect the tube to pressure. In this case water was        circulated at 37° C. (the vessel is not immersed).    -   2. Apply 0.1 bar, wait to stabilize and measure tube diameter        optically (camera+image analysis)    -   3. Increase pressure to 0.15 bar, wait to stabilize and measure        tube diameter    -   4. Calculate the compliance using these two points

The compliance coefficient is defined as:C=[(A_(s)−A_(d))/A_(d)]/[(P_(s)−P_(d))/P_(d)], where A_(s) and A_(d)are, respectively, the cross-sectional areas of systolic and diastoliclumens, and P_(s) and P_(d) are, respectively, systolic and diastolicpressure. The compliance coefficient for three-dimensional sampleprepared by AM was defined as:C=[(A_(M)−A_(m))/A_(m)]/[(P_(M)−P_(m))/P_(m)], where A_(M) and A_(m)are, respectively, the cross-sectional areas at minimum and maximumpressures, and P_(s) and P_(d) are, respectively, the minimum andmaximum pressures.

Table 5.8 provides the result of the compliance test for an Agilus30tube, 1.2 mm in wall thickness.

TABLE 5.8 Pressure [bar] 0.1 0.15 Diameter [mm] 9.10 9.28 Area [mm²]65.01 67.60 Compliance 0.12 Area Compliance[mm²/mmHg] 0.07

FIG. 35 and Table 5.9 summarize the compliance test for an Agilus30tube, 1.2 mm in wall thickness, as a function of the I.D.

TABLE 5.9 I.D. (mm) Compliance 6 0.19 8 0.28 10 0.31 20 0.87

FIG. 36 and Tables 5.10A-B summarize the compliance test for an Agilus30tube, I.D. 6 mm, as a function of the wall thickness, where FIG. 36 andTable 5.10A correspond to an experiment in which P_(m) was 0.1 bars andP_(M) was 0.15 bars, and Table 5.10B corresponds to an experiment inwhich P_(m) was 0 bars and P_(M) was 0.2 bars

TABLE 5.10A Wall Thickness (mm) Compliance 0.8 0.24 1 0.19 1.2 0.12

TABLE 5.10B Tube Compliance Agilus30 0.5 mm 0.73 Agilus30 0.6 mm 0.53Agilus30 0.7 mm 0.36 Agilus30 0.9 mm 0.22 Agilus30 1 mm 0.2 Tango 1 mm0.2

Time to Rupture (TTR)

In this study the TTR was measured according by applying a constantpressure and measuring the time to tube rupture and pressure drop. FIG.37 shows results of compliance and TTR measurements for various printedtubes.

Digital Material

The effect of the digital material used in the printing on thecompliance is summarized in FIG. 38 and Table 5.11 (see also Table 1.1,above).

TABLE 5.11 Tube Compliance BM61 core 0.5 0.08 BM61 core 0.43 0.21Agilus30\Tango 75\25 0.28 Pure Agilus30 0.08 Agilus30 5% BM 61 0.3Agilus 10% BM 61 0.35

Pulsation

The effect of pulsation on the TTR is summarized in Table 5.12. In Table5.12, WT is abbreviation to wall thickness.

TABLE 5.12 Constant Low High Pulsation pressure TTR Tube pressurepressure TTR (reference- WT (bar) (bar) Bpm [min] no pulsation) 0.6 0.20.3 60 ~15 <0.5 0.8 0.2 0.3 60 ~30 3.9 1 0.3 0.4 55 120 <1 1 0.1 0.15 60Over 12 H 1.2 0.3 0.4 55 Over 12 H

Comparison to Physiological Data

A comparison between the fabricated tubes and the philological data issummarized in table 5.13.

TABLE 5.13 Experimental Literature (Agilus30 on Difference Men WomenConnex3) Men Women Diastolic (75 mmHg, 0.1 Bar) 8.09 7.38 7.77 −3.9 5.3Diameter (mm) Systolic (120 mmHg, 0.15 Bar) 8.50 7.78 8.16 −4.0 4.9Diameter (mm) Diameter change (mm) 0.42 0.40 0.39 −6.0 −2.5 Intima mediathickness 0.70 0.65 0.72 2.9 11.6 (i.e. wall thickness) (mm) Compliance(area, normalized) 0.14 0.13 0.13 −9.7 2.5 (Unitless) Compliance (area)(mm{circumflex over ( )}2/mmHg) 0.29 0.30 0.28 −2.1 −6.9

Example 6 Exemplified Procedure for Obtaining Computer Object Data

The present Inventors devised a technique for preparing computer objectdata particularly useful for fabricating an object, such as, but notlimited to, a shelled and hollow object. The procedure is particularlyuseful for obtaining computer object data for use with system 10 orsystem 110. The exemplified procedure described in this example isuseful for fabricating shelled objects, such as, but not limited to,tubular structures, having a shell, an intermediate shell and a core,more particularly shelled objects wherein both the core and theintermediate shell are sacrificial. In some embodiments of the presentinvention procedure described in this example is used for fabricatingfrom non-biological materials objects featuring properties of a bodilystructure, such as, but not limited to, a structure comprising a softtissue. In these embodiments, the procedure described in this example isoptionally and preferably combined with the procedure described inExample 2, below.

FIG. 39A is a flowchart diagram of an exemplified procedure which can beused according to some embodiments of the present invention forexecuting operation 201 above. The procedure can be executed by a dataprocessor, such as, but not limited to, data processor 154 or 24.

The procedure begins at 750 and continues to 751 at which computerobject data describing a hollow shelled object, are received as input tothe procedure. A technique suitable for obtaining such computer objectdata is described in Example 2, below. The data at 751 optionally andpreferably describes a hollow object including only a shellencapsulation a void or voids referred to below as the cavity orcavities of the object. Thus, the data at 751 do not include datapertaining to a core or any intermediate shell within the shell.

The procedure continues to 752 at which computer object data describingthe cavities but not the shell are generated. The procedure continues to753 at which computer object data describing the cavities in shrunk formare generated. The cavities described by the data at 753 are shrunk inthe sense that their outermost surfaces encompass a volume which isreduced compared to the volume of the cavities received as input. Inother words, the cavities described by the data at 753 have an overalloutermost surface area that is smaller than the inner surface area ofthe hollow object described by the input data. A representative exampleof a technique suitable for being executed at 753 is described below.

The procedure continues to 754 at which computer object data obtained at751 are combined with the computer object data obtained at 753. Thiscombination provides combined computer object data that describe anoutermost shell encapsulating a core in a manner that there is a gapbetween the inner surface of the outermost shell and the outermostsurface of the core.

The procedure ends at 755.

The advantage of using this procedure for AM manufacturing of shelledand hollow objects is that it provides the AM system with sufficientinformation for dispensing the core, the shell, and an intermediateshell within the gap between the inner surface of the shell and theoutermost surface of the core.

In some embodiments of the present invention a user interface, such as,but not limited to, user interface 116 is used for receivinginstructions from the operator via a set of controls and for displayingvarious types of information and graphical descriptions during theexecution of the procedure. The data processor optionally and preferablydisplays progress messages and/or sends progress messages to a log file.

FIG. 39B is a screenshot of a graphical user interface (GUI) that can beused according to some embodiments of the present invention. In FIG.39B, the GUI shows that the input computer object data is an STL file,and that when this input is sliced its expected size is 0.29974 GB. TheGUI includes several controls. For example, the GUI includes a control,which, when activated, cause the data processor to load the inputcomputer object data (an STL file, in the present example). This controlis denoted “STL” in FIG. 39B. The GUI can also include a control, which,when activated, cause the data processor to compute and display on theGUI a rotatable and zoom-able preview of the computer object data. Thiscontrol is denoted “show” in FIG. 39B. FIG. 39C shows the result ofactivation of the “show” control for the case in which the of thecomputer object data describe a hollow labyrinth.

The GUI can also include a set of controls that cause the data processorto execute operations 752 and 753. For example, one control can causethe data processor to compute slices of the outermost shell, and anothercontrol can cause the data processor to generate computer object data ofthe cavities. These controls are denoted “slice” and “fill” in FIG. 39B.

FIG. 39D shows the GUI after activation of the “STL”, “slice” and “fill”controls. In this example, the computer object data that describe thecavities include 48248 faces. The “fill” control, causes the dataprocessor to perform three separate passes over the sliced faces, onepass for each of the three X, Y and Z dimensions.

The slicing operation can be by any technique known in the art of AM.Typically, for each face the processor finds all unique points on theface, optionally and preferably rounded to integer, collects all pointlocations from all faces, and optionally converts the point locationsinto a three-dimensional volumetric raster representation. Anothertechnique suitable for the present embodiments includes the use ofdistance field values, as further detailed in Example 2, below.

Operation 752 can by any technique known in the art of contractingthree-dimensional meshes. For example, in some embodiments of thepresent invention the “imfill” function of the Matlab® software isemployed, optionally and preferably with the “holes” option of thisfunction. The GUI can optionally be used to preview the sliced raster.This can be done by activating the “show” control. FIG. 39E shows theresult of activation of the “show” control after the activation of the“fill” control, for the case in which the of the computer object datadescribe a hollow labyrinth. This activation can optionally andpreferably receive input parameters, such as, but not limited to, thenumber of points to show in a point cloud.

The GUI can also include a set of controls that cause the data processorto execute operation 753. This set can be accessed by an access control,e.g., a tab selection control denoted by “Erode” in FIG. 39B. FIG. 39Fshows the GUI after activating the “Erode” tab in FIG. 39B. In thisexample, the set of controls comprises three controls that allow theoperator to select parameters to be used by the data processor toexecute operation 753. Alternatively or additionally these parametersmay have default values stored in a computer readable medium accessibleby the data process. These parameters include, erosion connectivity,indicating the number of neighbors to include in an erosion operation,the erosion method, and the axis to be used for the terminals. Theerosion connectivity can be from about 20 to about 30 neighbors, theerosion method can be selected from the group consisting of Euclidean,City Block, Chessboard, and Quasi-Euclidean, and the axis to be used forthe terminals can be selected from the group consisting of X, Y and Z.In FIG. 39F, which is not to be considered as limiting the selectederosion connectivity is neighbors, the selected erosion method isEuclidean, and the selected axis is Y.

The set of controls under the access control can also include a controlthat causes the data processor to find the inner-most points in thethree-dimensional volumetric raster representation. This controls aredenoted “erode” in FIG. 39F. Typically three-dimensional volumetricraster representation of about 15 mega-voxels yields about 2,000 erosionpoints. This operation can be done by any technique known in the artsuch as, but not limited to, the “bwulterode” function of the Matlab®software. The set of controls under the access control can also includea control which, when activated, cause the data processor to display theeroded points. This control is denoted “show” in FIG. 39F. FIG. 39Gshows the result of activation of the “show” control within the “Erode”tab, after the activation of the “erode” control within the “Erode” forthe case in which the of the computer object data describe a hollowlabyrinth. This activation can optionally and preferably receive inputparameters, such as, but not limited to, the number of points to show ina point cloud.

The set of controls under the access control can also include a controlthat causes the data processor to sort the eroded points so as to formlines. This control is denoted “sort” in FIG. 39F. In this operation,the data processor typically generates a connectivity list connectingpairs of points together, where the points in each pair are nearestneighbor points, and where there exists a connecting line such as astraight line through the filled raster between the pair of points, andalso while assuring that no point is connected to more than two others,so as to form connected lines.

The set of controls under the access control can also include a controlthat causes the data processor to identify which of the connected pointsare to be terminal points of the object. This control is denoted“terminals” in FIG. 39F. Alternatively, the data processor can identifythe terminal point automatically, for example by virtue of them beingextreme and isolated along a predetermined direction.

The set of controls under the access control can also include a controlthat causes the data processor to join the lines obtained during thesorting operation. This control is denoted “join” in FIG. 39F. When theinput computer object data describes a labyrinth, this operation isoptionally and preferably executed to form a labyrinth which is shrunkwith respect to the input labyrinth. In various exemplary embodiments ofthe invention the terminal points are excluded from this operation.Denoting the number of lines by L, and the number of terminal points byT, in this operation the data processor attempts to join 2L-T points.Typically, there are about 100 points per line, so if there is a totalof N points after the sorting operation, these points form about L=N/100lines and about T=N/200 terminal points. For an exemplified situation of2000 points after sorting, there are about 30 points to be joined.

According to some embodiments, the data processor finds, for each pointp of these points, another point q belonging to another line that isnear the point p, and that is connected in a similar fashion as it isconnected after to the sorting operation. When the data processor findstwo such points p and q, the data processor finds preferably connectsthese points, thereby forming a connected labyrinth.

When a line still remains unconnected to some others, the data processoroptionally and preferably attempts to connect any of the line'snon-terminal points to points belonging to other lines, and optionallyalso attempts to minimize the distance between connected points.

The data processor can optionally and preferably produce a rotatabledisplay showing the points joined to distinct but connected lines, andalso showing the terminal points, as depicted in FIG. 39H. The dataprocessor can also produce a table file listing the points sorted tolines, as shown in FIG. 39K.

The GUI can also include a set of controls that cause the data processorto generate an output pertaining the results of operation 754. This setcan be accessed by an access control, e.g., a tab selection controldenoted by “Output” in FIG. 39B.

FIG. 39I shows the GUI after activating the “Output” tab in FIG. 39B. Inthis example, the set of controls comprises a control that causes thedata processor to interpolate the individual points in each line so asto form continuous lines. This control is denoted “Continue” in FIG.39I. The interpolation can be a linear interpolation over pointlocations, while rounding to integers. Non-linear interpolation is alsocontemplated and is useful, for example, when the linear interpolationresults in outlier lines or points. In this example, the set of controlscomprises a control that causes the data processor to generate adistance map with the volume containing the cavities. This control isdenoted “Peel” in FIG. 39I. This step is optionally and preferablyperformed by parallel processing. The distances in the distance map aredistances between points in the computer object data describing thecavities and its nearest point in the computed lines, and optionally andpreferably also distances from the edge of the raster that is equivalentto the computer object data describing the cavities. In this example,the set of controls also comprises the set of controls comprisescontrols that allow the operator to select geometrical parameters to beused by the data processor to execute operation 753. These parameterscan include, for example, the maximum radius for the liquid support(which is half of the L_(MAX) parameter defined above, and the minimalthickness c_(MIN) of the intermediate layer. The set of controlsoptionally and preferably comprises a control that causes the dataprocessor to dilate the lines by an amount specified by the geometricalparameters. This control is denoted “Finalize” in FIG. 39I. The dilatedlines can be converted to mesh in any technique known in the art, suchas, but not limited to, the Marching Cubes algorithm, or the like. Theproduced mesh can then be output to a computer readable medium, e.g., asan STL file.

The resulting combined computer object data can be viewed by anycommercially available utility. Alternatively the data processor canco-display it with some previously calculated data using. FIG. 39J showsthe result of activation of the “Finalize” control for the case in whichthe of the computer object data describe a hollow labyrinth.

Although the invention has been described in conjunction with specificembodiments thereof, it is evident that many alternatives, modificationsand variations will be apparent to those skilled in the art.Accordingly, it is intended to embrace all such alternatives,modifications and variations that fall within the spirit and broad scopeof the appended claims.

It is the intent of the applicant(s) that all publications, patents andpatent applications referred to in this specification are to beincorporated in their entirety by reference into the specification, asif each individual publication, patent or patent application wasspecifically and individually noted when referenced that it is to beincorporated herein by reference. In addition, citation oridentification of any reference in this application shall not beconstrued as an admission that such reference is available as prior artto the present invention. To the extent that section headings are used,they should not be construed as necessarily limiting. In addition, anypriority document(s) of this application is/are hereby incorporatedherein by reference in its/their entirety.

What is claimed is:
 1. A tubular structure fabricated by additivemanufacturing from non-biological building material formulations, andcomprising: an elongated core, a shell encapsulating said core and anintermediate shell between said core and said shell, each of said core,said shell and said intermediate shell being made of a differentmaterial or a different combination of materials, wherein both said coreand said intermediate shell are sacrificial, and wherein one of saidintermediate shell and said core is made of a hardened support material,and another one of said intermediate shell and said core is made of aliquid or liquid-like material.
 2. The tubular structure of claim 1,wherein said intermediate shell is made of said hardened supportmaterial, and said core is made of said liquid or liquid-like material.3. The tubular structure of claim 1, wherein said core is made of saidhardened support material, and said intermediate shell is made of saidliquid or liquid-like material.
 4. The tubular structure according toclaim 2, wherein said liquid or liquid-like material is characterized byat least one of: a viscosity of no more than 10000 centipoises; Shearloss modulus to Shear storage modulus ratio greater than 1; a Shearmodulus lower than 20 kPa; flowability when subjected to a positivepressure of no more than 1 bar; a shear-thinning and/or thixotropicbehavior; and a thermal-thinning behavior.
 5. The tubular structureaccording to claim 1, having a shape of a blood vessel.
 6. The tubularstructure according to claim 1, wherein said shell is embedded in asupporting structure.
 7. The tubular structure according to claim 6,wherein said supporting structure is sacrificial.
 8. An objectfabricated by additive manufacturing from non-biological buildingmaterial formulations, the object has a shape of an organ andcomprising: at least one structure having a shape of a blood vessel andat least one structure having a shape of a bodily structure other than ablood vessel, wherein said structure having said shape of said bloodvessel is the tubular structure according to claim
 1. 9. An objectfabricated by additive manufacturing from non-biological buildingmaterial formulations, the object comprises an interconnected network ofelongated structures, each having a shape of a blood vessel and beingaccording to claim
 1. 10. The tubular structure according to claim 1,further comprising reinforcing elements embedded in said shell.
 11. Thetubular structure according to claim 10, wherein said reinforcingelements are oriented to effect anisotropic mechanical properties ofsaid shell.
 12. The tubular structure according to claim 10, whereinsaid reinforcing elements comprise at least one elongated reinforcingelement embedded in said shell parallel to a longitudinal axis of saidshell.
 13. The tubular structure according to claim 10, wherein saidreinforcing elements comprise at least one annular reinforcing elementembedded in said shell along an azimuthal direction defining said shell.14. The tubular structure according to claim 13, wherein saidreinforcing elements comprise at least one elongated reinforcing elementembedded in said shell parallel to a longitudinal axis of said shell.15. The tubular structure according to claim 10, wherein saidreinforcing elements are made of a material having a tensile strength offrom about 2 to about 4 MPa according to ASTM D-412.
 16. The tubularstructure according to claim 10, wherein said reinforcing elements aremade of a material having a Shore A hardness from about 25 MPa to about35 MPa according to ASTM D-224D.
 17. The tubular structure according toclaim 10, wherein said reinforcing elements are made of a material whichcomprises an elastomeric curable material and silica particles.
 18. Thetubular structure according to claim 1, further comprising a liner layerat least partially coating an inner surface of said shell, between saidintermediate shell and said inner surface, wherein an attachment betweensaid liner layer and said shell is stronger than an attachment betweensaid intermediate shell and said liner layer.
 19. The tubular structureor object according to claim 15, wherein said liner layer is harder thansaid shell.
 20. The tubular structure or object according to claim 15,wherein said liner layer has mechanical properties of plaque tissue.